The double-threshold autoregressive conditional heteroscedastic(DTARCH) model is a useful tool to measure and forecast the mean and volatility of an asset return in a financial time series. The DTARCH model can handle...The double-threshold autoregressive conditional heteroscedastic(DTARCH) model is a useful tool to measure and forecast the mean and volatility of an asset return in a financial time series. The DTARCH model can handle situations wherein the conditional mean and conditional variance specifications are piecewise linear based on previous information. In practical applications, it is important to check whether the model has a double threshold for the conditional mean and conditional heteroscedastic variance. In this study, we develop a likelihood ratio test based on the estimated residual error for the hypothesis testing of DTARCH models. We first investigate DTARCH models with restrictions on parameters and propose the unrestricted and restricted weighted composite quantile regression(WCQR) estimation for the model parameters. These estimators can be used to construct the likelihood ratio-type test statistic. We establish the asymptotic results of the WCQR estimators and asymptotic distribution of the proposed test statistics. The finite sample performance of the proposed WCQR estimation and the test statistic is shown to be acceptable and promising using simulation studies. We use two real datasets derived from the Shanghai and Shenzhen Composite Indexes to illustrate the methodology.展开更多
Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields.In this paper,a reducing component procedure is proposed for es- timating the unknown functions...Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields.In this paper,a reducing component procedure is proposed for es- timating the unknown functions and their derivatives in very general models,in which the unknown coefficient functions admit different or the same degrees of smoothness and the covariates can be time- dependent.The asymptotic properties of the estimators,such as consistency,rate of convergence and asymptotic distribution,are derived.The asymptotic results show that the asymptotic variance of the reducing component estimators is smaller than that of the existing estimators when the coefficient functions admit different degrees of smoothness.Finite sample properties of our procedures are studied through Monte Carlo simulations.展开更多
In practice, some sensors of aircraft engines naturally fail to obtain an acceptable measurement for control propose, which will severely degrade the system performance and even deactivate the limit protection functio...In practice, some sensors of aircraft engines naturally fail to obtain an acceptable measurement for control propose, which will severely degrade the system performance and even deactivate the limit protection function. This paper proposes an adaptive strategy for the limit protection task under unreliable measurement. With the help of a nominal system, an online estimator with gradient adaption law and low-pass filter is devised to evaluate output uncertainty.Based on the estimation result, a sliding mode controller is designed by defining a sliding surface and deriving a control law. Using Lyapunov theorem, the stability of the online estimator and the closed-loop system is detailedly proven. Simulations based on a reliable turbofan model are presented, which verify the stability and effectiveness of the proposed method. Simulation results show that the online estimator can operate against the measurement noise, and the sliding controller can keep relevant outputs within their limits despite slow-response sensors.展开更多
Edge preserved smoothing techniques have gained importance for the purpose of image processing applications A good edge preserving filter is given by nonlocal-means filter rather than any other linear model based appr...Edge preserved smoothing techniques have gained importance for the purpose of image processing applications A good edge preserving filter is given by nonlocal-means filter rather than any other linear model based approaches. This paper explores a different approach of nonlocal-means filter by using robust M-estimator function rather than the exponential function for its weight calculation. Here the filter output at each pixel is the weighted average of pixels with surrounding neighborhoods using the chosen robust M-estimator function. The main direction of this paper is to identify the best robust M-estimator function for nonlocal-means denoising algorithm. In order to speed up the computation, a new patch classification method is followed to eliminate the uncorrelated patches from the weighted averaging process. This patch classification approach compares favorably to existing techniques in respect of quality versus computational time. Validations using standard test images and brain atlas images have been analyzed and the results were compared with the other known methods. It is seen that there is reason to believe that the proposed refined technique has some notable points.展开更多
We introduce a four-parameter lifetime distribution called the odd log-logistic generalized Gompertz model to generalize the exponential,generalized exponential and generalized Gompertz distributions,among others.We o...We introduce a four-parameter lifetime distribution called the odd log-logistic generalized Gompertz model to generalize the exponential,generalized exponential and generalized Gompertz distributions,among others.We obtain explicit expressions for themoments,moment-generating function,asymptotic distribution,quantile function,mean deviations and distribution of order statistics.The method of maximum likelihood estimation of parameters is compared by six different methods of estimations with simulation study.The applicability of the new model is illustrated by means of a real data set.展开更多
This paper describes a data reconstruction technique for a multi-function sensor based on the Mestimator, which uses least squares and weighted least squares method. The algorithm has better robustness than convention...This paper describes a data reconstruction technique for a multi-function sensor based on the Mestimator, which uses least squares and weighted least squares method. The algorithm has better robustness than conventional least squares which can amplify the errors of inaccurate data. The M-estimator places particular emphasis on reducing the effects of large data errors, which are further overcome by an iterative regression process which gives small weights to large off-group data errors and large weights to small data errors. Simulation results are consistent with the hypothesis with 81 groups of regression data having an average accuracy of 3.5%, which demonstrates that the M-estimator provides more accurate and reliable data reconstruction.展开更多
The author obtains the rate of strong convergence,mean squared error and optimal choice of the“smoothing parameter”(the sample fraction)of a tail index estimator which was proposed by the author from Pickands’estim...The author obtains the rate of strong convergence,mean squared error and optimal choice of the“smoothing parameter”(the sample fraction)of a tail index estimator which was proposed by the author from Pickands’estimator,and called modified Pickands’estimator.The similar results about Hill’s estimator are also obtained,which generalize the corresponding results in.Besides,some comparisons between Hill’s estimator and the modified Pickands’estimator are given.展开更多
Model selection strategies have been routinely employed to determine a model for data analysis in statistics, and further study and inference then often proceed as though the selected model were the true model that we...Model selection strategies have been routinely employed to determine a model for data analysis in statistics, and further study and inference then often proceed as though the selected model were the true model that were known a priori. Model averaging approaches, on the other hand, try to combine estimators for a set of candidate models. Specifically, instead of deciding which model is the 'right' one, a model averaging approach suggests to fit a set of candidate models and average over the estimators using data adaptive weights.In this paper we establish a general frequentist model averaging framework that does not set any restrictions on the set of candidate models. It broaden, the scope of the existing methodologies under the frequentist model averaging development. Assuming the data is from an unknown model, we derive the model averaging estimator and study its limiting distributions and related predictions while taking possible modeling biases into account.We propose a set of optimal weights to combine the individual estimators so that the expected mean squared error of the average estimator is minimized. Simulation studies are conducted to compare the performance of the estimator with that of the existing methods. The results show the benefits of the proposed approach over traditional model selection approaches as well as existing model averaging methods.展开更多
This paper considers a nonparametric varying coefficient regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the coefficient functions. Unde...This paper considers a nonparametric varying coefficient regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the coefficient functions. Under mild regularity assumptions,the global convergence rates of the B-spline estimators of the unknown coefficient functions are established. Asymptotic results show that our B-spline estimators achieve the optimal convergence rate. The asymptotic distributions of the B-spline estimators of the unknown coefficient functions are also derived. A procedure for selecting smoothing parameters is given. Finite sample properties of our procedures are studied through Monte Carlo simulations. Application of the proposed method is demonstrated by examining voting behaviors across US counties in the 1980 presidential election.展开更多
Estimations of parametric functions under a system of linear regression equations with correlated errors across equations involve many complicated operations of matrices and their generalized inverses. In the past sev...Estimations of parametric functions under a system of linear regression equations with correlated errors across equations involve many complicated operations of matrices and their generalized inverses. In the past several years, a useful tool -- the matrix rank method was utilized to simplify various complicated operations of matrices and their generalized inverses. In this paper, we use the matrix rank method to derive a variety of new algebraic and statistical properties for the best linear unbiased estimators （BLUEs） of parametric functions under the system. In particular, we give the necessary and sufficient conditions for some equalities, additive and block decompositions of BLUEs of parametric functions under the system to hold.展开更多
We introduce a new two-parameter model related to the inverted Topp–Leone distribution called the power inverted Topp–Leone(PITL)distribution.Major properties of the PITL distribution are stated;including;quantile m...We introduce a new two-parameter model related to the inverted Topp–Leone distribution called the power inverted Topp–Leone(PITL)distribution.Major properties of the PITL distribution are stated;including;quantile measures,moments,moment generating function,probability weighted moments,Bonferroni and Lorenz curve,stochastic ordering,incomplete moments,residual life function,and entropy measure.Acceptance sampling plans are developed for the PITL distribution,when the life test is truncated at a pre-specified time.The truncation time is assumed to be the median lifetime of the PITL distribution with pre-specified factors.The minimum sample size necessary to ensure the specified life test is obtained under a given consumer’s risk.Numerical results for given consumer’s risk,parameters of the PITL distribution and the truncation time are obtained.The estimation of the model parameters is argued using maximum likelihood,least squares,weighted least squares,maximum product of spacing and Bayesian methods.A simulation study is confirmed to evaluate and compare the behavior of different estimates.Two real data applications are afforded in order to examine the flexibility of the proposed model compared with some others distributions.The results show that the power inverted Topp–Leone distribution is the best according to the model selection criteria than other competitive models.展开更多
A new technique of residual-type a posteriori error analysis is developed for the lowest- order Raviart-Thomas mixed finite element discretizations of convection-diffusion-reaction equations in two- or three-dimension...A new technique of residual-type a posteriori error analysis is developed for the lowest- order Raviart-Thomas mixed finite element discretizations of convection-diffusion-reaction equations in two- or three-dimension. Both centered mixed scheme and upwind-weighted mixed scheme are considered. The a posteriori error estimators, derived for the stress variable error plus scalar displacement error in L_2-norm, can be directly computed with the solutions of the mixed schemes without any additional cost, and are proven to be reliable. Local efficiency dependent on local variations in coefficients is obtained without any saturation assumption, and holds from the cases where convection or reaction is not present to convection- or reaction-dominated problems. The main tools of the analysis are the postprocessed approximation of scalar displacement, abstract error estimates, and the property of modified Oswald interpolation. Numerical experiments are carried out to support our theoretical results and to show the competitive behavior of the proposed posteriori error estimates.展开更多
This paper is an extension and generalization of the study carried out by [1] on the estimation of the population ratio (R) of the population means of two variables (y and x) under Simple Random Sampling (SRS) scheme,...This paper is an extension and generalization of the study carried out by [1] on the estimation of the population ratio (R) of the population means of two variables (y and x) under Simple Random Sampling (SRS) scheme, using a variable transformation of the auxiliary variable, x. All the six estimators proposed by [1] are easily identified as special cases of the proposed class of estimators. Asymptotic properties of the proposed class of estimators are derived theoretically and subsequently verified using empirical illustrations. Some of the proposed estimators are found to have relatively large gains in efficiency over the customary ratio estimator, ?for the given data set.展开更多
In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initial value problem for a nonlinear Volterra in...In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initial value problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of posteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.展开更多
Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcom...Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcomes. This paper focuses on the maximum likelihood estimation of joint location and scale models of the skew-normal distribution. The proposed procedure can simultaneously estimate parameters in the location model and the scale model. Simulation studies and a real example are used to illustrate the proposed methodologies.展开更多
In this article,we consider a new family of exponential type estimators for estimating the unknown population mean of the study variable.We propose estimators taking advantage of the auxiliary variable information und...In this article,we consider a new family of exponential type estimators for estimating the unknown population mean of the study variable.We propose estimators taking advantage of the auxiliary variable information under the first and second non-response cases separately.The required theoretical comparisons are obtained and the numerical studies are conducted.In conclusion,the results show that the proposed family of estimators is the most efficient estimator with respect to the estimators in literature under the obtained conditions for both cases.展开更多
基金supported by National Natural Science Foundation of China(Grant No.71601123)MOE(Ministry of Education in China)Project of Humanities and Social Sciences(Grant No.15YJC910004)+3 种基金supported by National Natural Science Foundation of China(Grant No.11471277)the Research Grant Council of the Hong Kong Special Administration Region(Grant No.GRF14305014)supported by the State Key Program of National Natural Science Foundation of China(Grant No.71331006)the Major Research Plan of National Natural Science Foundation of China(Grant No.91546202)
文摘The double-threshold autoregressive conditional heteroscedastic(DTARCH) model is a useful tool to measure and forecast the mean and volatility of an asset return in a financial time series. The DTARCH model can handle situations wherein the conditional mean and conditional variance specifications are piecewise linear based on previous information. In practical applications, it is important to check whether the model has a double threshold for the conditional mean and conditional heteroscedastic variance. In this study, we develop a likelihood ratio test based on the estimated residual error for the hypothesis testing of DTARCH models. We first investigate DTARCH models with restrictions on parameters and propose the unrestricted and restricted weighted composite quantile regression(WCQR) estimation for the model parameters. These estimators can be used to construct the likelihood ratio-type test statistic. We establish the asymptotic results of the WCQR estimators and asymptotic distribution of the proposed test statistics. The finite sample performance of the proposed WCQR estimation and the test statistic is shown to be acceptable and promising using simulation studies. We use two real datasets derived from the Shanghai and Shenzhen Composite Indexes to illustrate the methodology.
基金Research Foundation for Doctor Programme (Grant No.20060254006)the National Natural Science Foundation of China (Grant No.10671089)
文摘Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields.In this paper,a reducing component procedure is proposed for es- timating the unknown functions and their derivatives in very general models,in which the unknown coefficient functions admit different or the same degrees of smoothness and the covariates can be time- dependent.The asymptotic properties of the estimators,such as consistency,rate of convergence and asymptotic distribution,are derived.The asymptotic results show that the asymptotic variance of the reducing component estimators is smaller than that of the existing estimators when the coefficient functions admit different degrees of smoothness.Finite sample properties of our procedures are studied through Monte Carlo simulations.
文摘In practice, some sensors of aircraft engines naturally fail to obtain an acceptable measurement for control propose, which will severely degrade the system performance and even deactivate the limit protection function. This paper proposes an adaptive strategy for the limit protection task under unreliable measurement. With the help of a nominal system, an online estimator with gradient adaption law and low-pass filter is devised to evaluate output uncertainty.Based on the estimation result, a sliding mode controller is designed by defining a sliding surface and deriving a control law. Using Lyapunov theorem, the stability of the online estimator and the closed-loop system is detailedly proven. Simulations based on a reliable turbofan model are presented, which verify the stability and effectiveness of the proposed method. Simulation results show that the online estimator can operate against the measurement noise, and the sliding controller can keep relevant outputs within their limits despite slow-response sensors.
文摘Edge preserved smoothing techniques have gained importance for the purpose of image processing applications A good edge preserving filter is given by nonlocal-means filter rather than any other linear model based approaches. This paper explores a different approach of nonlocal-means filter by using robust M-estimator function rather than the exponential function for its weight calculation. Here the filter output at each pixel is the weighted average of pixels with surrounding neighborhoods using the chosen robust M-estimator function. The main direction of this paper is to identify the best robust M-estimator function for nonlocal-means denoising algorithm. In order to speed up the computation, a new patch classification method is followed to eliminate the uncorrelated patches from the weighted averaging process. This patch classification approach compares favorably to existing techniques in respect of quality versus computational time. Validations using standard test images and brain atlas images have been analyzed and the results were compared with the other known methods. It is seen that there is reason to believe that the proposed refined technique has some notable points.
文摘We introduce a four-parameter lifetime distribution called the odd log-logistic generalized Gompertz model to generalize the exponential,generalized exponential and generalized Gompertz distributions,among others.We obtain explicit expressions for themoments,moment-generating function,asymptotic distribution,quantile function,mean deviations and distribution of order statistics.The method of maximum likelihood estimation of parameters is compared by six different methods of estimations with simulation study.The applicability of the new model is illustrated by means of a real data set.
基金the National Natural Science Foundation of China (Nos. 60172071 and 60372005)
文摘This paper describes a data reconstruction technique for a multi-function sensor based on the Mestimator, which uses least squares and weighted least squares method. The algorithm has better robustness than conventional least squares which can amplify the errors of inaccurate data. The M-estimator places particular emphasis on reducing the effects of large data errors, which are further overcome by an iterative regression process which gives small weights to large off-group data errors and large weights to small data errors. Simulation results are consistent with the hypothesis with 81 groups of regression data having an average accuracy of 3.5%, which demonstrates that the M-estimator provides more accurate and reliable data reconstruction.
文摘The author obtains the rate of strong convergence,mean squared error and optimal choice of the“smoothing parameter”(the sample fraction)of a tail index estimator which was proposed by the author from Pickands’estimator,and called modified Pickands’estimator.The similar results about Hill’s estimator are also obtained,which generalize the corresponding results in.Besides,some comparisons between Hill’s estimator and the modified Pickands’estimator are given.
基金supported by National Science Foundation of USA (Grant Nos.DMS1812048,DMS-1737857,DMS-1513483 and DMS-1418042)National Natural Science Foundation of China (Grant No.11529101)
文摘Model selection strategies have been routinely employed to determine a model for data analysis in statistics, and further study and inference then often proceed as though the selected model were the true model that were known a priori. Model averaging approaches, on the other hand, try to combine estimators for a set of candidate models. Specifically, instead of deciding which model is the 'right' one, a model averaging approach suggests to fit a set of candidate models and average over the estimators using data adaptive weights.In this paper we establish a general frequentist model averaging framework that does not set any restrictions on the set of candidate models. It broaden, the scope of the existing methodologies under the frequentist model averaging development. Assuming the data is from an unknown model, we derive the model averaging estimator and study its limiting distributions and related predictions while taking possible modeling biases into account.We propose a set of optimal weights to combine the individual estimators so that the expected mean squared error of the average estimator is minimized. Simulation studies are conducted to compare the performance of the estimator with that of the existing methods. The results show the benefits of the proposed approach over traditional model selection approaches as well as existing model averaging methods.
基金supported by National Natural Science Foundation of China (Grant No. 10671089)China Postdoctoral Science Foundation and Jiangsu Planned Projects for Postdoctoral Research Funds
文摘This paper considers a nonparametric varying coefficient regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the coefficient functions. Under mild regularity assumptions,the global convergence rates of the B-spline estimators of the unknown coefficient functions are established. Asymptotic results show that our B-spline estimators achieve the optimal convergence rate. The asymptotic distributions of the B-spline estimators of the unknown coefficient functions are also derived. A procedure for selecting smoothing parameters is given. Finite sample properties of our procedures are studied through Monte Carlo simulations. Application of the proposed method is demonstrated by examining voting behaviors across US counties in the 1980 presidential election.
基金Supported by National Natural Science Foundation of China (Grant No. 70871073)
文摘Estimations of parametric functions under a system of linear regression equations with correlated errors across equations involve many complicated operations of matrices and their generalized inverses. In the past several years, a useful tool -- the matrix rank method was utilized to simplify various complicated operations of matrices and their generalized inverses. In this paper, we use the matrix rank method to derive a variety of new algebraic and statistical properties for the best linear unbiased estimators （BLUEs） of parametric functions under the system. In particular, we give the necessary and sufficient conditions for some equalities, additive and block decompositions of BLUEs of parametric functions under the system to hold.
文摘We introduce a new two-parameter model related to the inverted Topp–Leone distribution called the power inverted Topp–Leone(PITL)distribution.Major properties of the PITL distribution are stated;including;quantile measures,moments,moment generating function,probability weighted moments,Bonferroni and Lorenz curve,stochastic ordering,incomplete moments,residual life function,and entropy measure.Acceptance sampling plans are developed for the PITL distribution,when the life test is truncated at a pre-specified time.The truncation time is assumed to be the median lifetime of the PITL distribution with pre-specified factors.The minimum sample size necessary to ensure the specified life test is obtained under a given consumer’s risk.Numerical results for given consumer’s risk,parameters of the PITL distribution and the truncation time are obtained.The estimation of the model parameters is argued using maximum likelihood,least squares,weighted least squares,maximum product of spacing and Bayesian methods.A simulation study is confirmed to evaluate and compare the behavior of different estimates.Two real data applications are afforded in order to examine the flexibility of the proposed model compared with some others distributions.The results show that the power inverted Topp–Leone distribution is the best according to the model selection criteria than other competitive models.
基金The authors are grateful for the anonymous referees for their helpful com- ments. This work was supported in part by The Education Science Foundation of Chongqing （KJ120420）, National Natural Science Foundation of China （11171239）, The Project-sponsored by Scientific Research Foundation for the Returned Overseas Chinese Scholars and Open Fund of Key Laboratory of Mountain Hazards and Earth Surface Processes, CAS.
文摘A new technique of residual-type a posteriori error analysis is developed for the lowest- order Raviart-Thomas mixed finite element discretizations of convection-diffusion-reaction equations in two- or three-dimension. Both centered mixed scheme and upwind-weighted mixed scheme are considered. The a posteriori error estimators, derived for the stress variable error plus scalar displacement error in L_2-norm, can be directly computed with the solutions of the mixed schemes without any additional cost, and are proven to be reliable. Local efficiency dependent on local variations in coefficients is obtained without any saturation assumption, and holds from the cases where convection or reaction is not present to convection- or reaction-dominated problems. The main tools of the analysis are the postprocessed approximation of scalar displacement, abstract error estimates, and the property of modified Oswald interpolation. Numerical experiments are carried out to support our theoretical results and to show the competitive behavior of the proposed posteriori error estimates.
文摘This paper is an extension and generalization of the study carried out by [1] on the estimation of the population ratio (R) of the population means of two variables (y and x) under Simple Random Sampling (SRS) scheme, using a variable transformation of the auxiliary variable, x. All the six estimators proposed by [1] are easily identified as special cases of the proposed class of estimators. Asymptotic properties of the proposed class of estimators are derived theoretically and subsequently verified using empirical illustrations. Some of the proposed estimators are found to have relatively large gains in efficiency over the customary ratio estimator, ?for the given data set.
基金This work is supported partially by SRF for ROCS, SEM, NSERC (Canada) and NSF grant DMS-9704621.
文摘In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initial value problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of posteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.
基金Supported by the National Natural Science Foundation of China(11261025,11201412)the Natural Science Foundation of Yunnan Province(2011FB016)the Program for Middle-aged Backbone Teacher,Yunnan University
文摘Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcomes. This paper focuses on the maximum likelihood estimation of joint location and scale models of the skew-normal distribution. The proposed procedure can simultaneously estimate parameters in the location model and the scale model. Simulation studies and a real example are used to illustrate the proposed methodologies.
文摘In this article,we consider a new family of exponential type estimators for estimating the unknown population mean of the study variable.We propose estimators taking advantage of the auxiliary variable information under the first and second non-response cases separately.The required theoretical comparisons are obtained and the numerical studies are conducted.In conclusion,the results show that the proposed family of estimators is the most efficient estimator with respect to the estimators in literature under the obtained conditions for both cases.
