This paper is concerned with tile proOlenl or improving hue ~lma^u~ u~ under Stein＇s loss. By the partial Iwasawa coordinates of covariance matrix, the corresponding risk can be split into three parts. One can use th...This paper is concerned with tile proOlenl or improving hue ~lma^u~ u~ under Stein＇s loss. By the partial Iwasawa coordinates of covariance matrix, the corresponding risk can be split into three parts. One can use the information in the weighted matrix of weighted quadratic loss to improve one part of risk. However, this paper indirectly takes advantage of the information in the sample mean and reuses Iwasawa coordinates to improve the rest of risk. It is worth mentioning that the process above can be repeated. Finally, a Monte Carlo simulation study is carried out to verify the theoretical results.展开更多
We consider estimation of the scale parameter of a two-parameter exponential distribution on the basis of doubly censored data.Classes of estimators,improving upon the minimum risk equivariant estimator,are derived un...We consider estimation of the scale parameter of a two-parameter exponential distribution on the basis of doubly censored data.Classes of estimators,improving upon the minimum risk equivariant estimator,are derived under an arbitrary strictly convex loss function.Some existing dominating procedures are shown to belong to the proposed classes of estimators.展开更多
This paper considers the effect of an erroneous inclusion of regressors on the risk propertiesof the Stein-rule,positive-part Stein-rule and inequality restricted and pre-test estimators in a linearregression model.Th...This paper considers the effect of an erroneous inclusion of regressors on the risk propertiesof the Stein-rule,positive-part Stein-rule and inequality restricted and pre-test estimators in a linearregression model.The two Stein-rule estimators are considered when extraneous information is availablein the form of a set of multiple equality constraints on the coefficients,while the inequality estimatorsare considered under the case of a single inequality constraint.It is shown that the inclusion ofwrong regressors has only minimal effect on the properties of the Stein-rule and positive-part Stein-ruleestimators,and no effect at all on the inequality restricted and pre-test estimators when there is asingle inequality constraint.展开更多
A reliability-growth test is often used to assess complex systems under development.Reliability-growth models are usually used to quantify the achievable reliability indices and predict the expected reliability values...A reliability-growth test is often used to assess complex systems under development.Reliability-growth models are usually used to quantify the achievable reliability indices and predict the expected reliability values.The Crow army-materiel-system-analysis-activity(Crow-AMSAA)projection model and the AMSAA maturity projection(AMPM)-Stein model are suitable for modelling delayed corrective strategies.The AMPM-Stein model,which involves more failure data and requires limited assumptions,is more robust than the Crow-AMSAA projection model.However,the rationality of the Stein factor introduced in the AMPM-Stein model has always been controversial.An AMPM-Stein extended projection model,derived from data regrouping based on similar failure mechanisms,is presented to alleviate the problem.The study demonstrated that the proposed model performed well,the prediction results were credible,and the robustness of the proposed model was examined.Furthermore,the Stein-shrinkage factors,which are derived from components with similar inherent failure mechanisms,are easier to understand and accept in the field of engineering.An example shows that the proposed model is more suitable and accurate than the Crow-AMSAA model and the AMPM-Stein model,by comparing the projection values based on the failure data of the previous phases with the actual values of the current phases.This study provides a technical basis for extensive applications of the proposed model.展开更多
The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for thes...The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for these types of estimators in several common settings. These results provide efficient ways of comparing different estimators and eliciting tuning parameters. Moreover, our analyses reveal new insights on the behavior of these low rank matrix estimators. These observations are of great theoretical and practical importance. In particular, they suggest that, contrary to conventional wisdom, for rank constrained estimators the total number of free parameters underestimates the degrees of freedom, whereas for nuclear norm penalization, it overestimates the degrees of freedom. In addition, when using most model selection criteria to choose the tuning parameter for nuclear norm penalization, it oftentimes suffices to entertain a finite number of candidates as opposed to a continuum of choices. Numerical examples are also presented to illustrate the practical implications of our results.展开更多
This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both ...This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.展开更多
In this paper, we explore the properties of a positive-part Stein-like estimator which is a stochastically weighted convex combination of a fully correlated parameter model estimator and uncorrelated parameter model e...In this paper, we explore the properties of a positive-part Stein-like estimator which is a stochastically weighted convex combination of a fully correlated parameter model estimator and uncorrelated parameter model estimator in the Random Parameters Logit (RPL) model. The results of our Monte Carlo experiments show that the positive-part Stein-like estimator provides smaller MSE than the pretest estimator in the fully correlated RPL model. Both of them outperform the fully correlated RPL model estimator and provide more accurate information on the share of population putting a positive or negative value on the alternative attributes than the fully correlated RPL model estimates. The Monte Carlo mean estimates of direct elasticity with pretest and positive-part Stein-like estimators are closer to the true value and have smaller standard errors than those with fully correlated RPL model estimator.展开更多
An effective de-noising method for fiber optic gyroscopes （FOGs） is proposed. This method is based on second-generation Daubechies D4 （DB4） wavelet transform （WT） and level-dependent threshold estimator called S...An effective de-noising method for fiber optic gyroscopes （FOGs） is proposed. This method is based on second-generation Daubechies D4 （DB4） wavelet transform （WT） and level-dependent threshold estimator called Stein＇s unbiased risk estimator （SURE）. The whole approach consists of three critical parts： wavelet decomposition module, parameters estimation module and SURE de-noising module. First, DB4 wavelet is selected as lifting base of the second-generation wavelet in the decomposition module. Second, in the parameters estimation module, maximum likelihood estimation （MLE） is used for stochastic noise parameters estimation. Third, combined with soft threshold de-noising technique, the SURE de-noising module is designed. For comparison, both the traditional universal threshold wavelet and the second-generation Harr wavelet method are also investigated. The experiment results show that the computation cost is 40% less than that of the traditional wavelet method. The standard deviation of de-noised FOG signal is 0.012 and the three noise terms such as angle random walk, bias instability and quantization noise are reduced to 0.007 2°/√h, 0.004 1° / h, and 0.008 1°, respectively.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.11371236the Graduate Student Innovation Foundation of Shanghai University of Finance and Economics(CXJJ-2015-440)
文摘This paper is concerned with tile proOlenl or improving hue ~lma^u~ u~ under Stein＇s loss. By the partial Iwasawa coordinates of covariance matrix, the corresponding risk can be split into three parts. One can use the information in the weighted matrix of weighted quadratic loss to improve one part of risk. However, this paper indirectly takes advantage of the information in the sample mean and reuses Iwasawa coordinates to improve the rest of risk. It is worth mentioning that the process above can be repeated. Finally, a Monte Carlo simulation study is carried out to verify the theoretical results.
文摘We consider estimation of the scale parameter of a two-parameter exponential distribution on the basis of doubly censored data.Classes of estimators,improving upon the minimum risk equivariant estimator,are derived under an arbitrary strictly convex loss function.Some existing dominating procedures are shown to belong to the proposed classes of estimators.
基金support provided by a General Research Fund under Grant No.9041467 from the Hong Kong Research Grant Council
文摘This paper considers the effect of an erroneous inclusion of regressors on the risk propertiesof the Stein-rule,positive-part Stein-rule and inequality restricted and pre-test estimators in a linearregression model.The two Stein-rule estimators are considered when extraneous information is availablein the form of a set of multiple equality constraints on the coefficients,while the inequality estimatorsare considered under the case of a single inequality constraint.It is shown that the inclusion ofwrong regressors has only minimal effect on the properties of the Stein-rule and positive-part Stein-ruleestimators,and no effect at all on the inequality restricted and pre-test estimators when there is asingle inequality constraint.
基金National Science and Technology Major Project of China(No.2019ZX04006001)。
文摘A reliability-growth test is often used to assess complex systems under development.Reliability-growth models are usually used to quantify the achievable reliability indices and predict the expected reliability values.The Crow army-materiel-system-analysis-activity(Crow-AMSAA)projection model and the AMSAA maturity projection(AMPM)-Stein model are suitable for modelling delayed corrective strategies.The AMPM-Stein model,which involves more failure data and requires limited assumptions,is more robust than the Crow-AMSAA projection model.However,the rationality of the Stein factor introduced in the AMPM-Stein model has always been controversial.An AMPM-Stein extended projection model,derived from data regrouping based on similar failure mechanisms,is presented to alleviate the problem.The study demonstrated that the proposed model performed well,the prediction results were credible,and the robustness of the proposed model was examined.Furthermore,the Stein-shrinkage factors,which are derived from components with similar inherent failure mechanisms,are easier to understand and accept in the field of engineering.An example shows that the proposed model is more suitable and accurate than the Crow-AMSAA model and the AMPM-Stein model,by comparing the projection values based on the failure data of the previous phases with the actual values of the current phases.This study provides a technical basis for extensive applications of the proposed model.
基金supported by National Science Foundation of USA (Grant No. DMS1265202)National Institutes of Health of USA (Grant No. 1-U54AI117924-01)
文摘The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for these types of estimators in several common settings. These results provide efficient ways of comparing different estimators and eliciting tuning parameters. Moreover, our analyses reveal new insights on the behavior of these low rank matrix estimators. These observations are of great theoretical and practical importance. In particular, they suggest that, contrary to conventional wisdom, for rank constrained estimators the total number of free parameters underestimates the degrees of freedom, whereas for nuclear norm penalization, it overestimates the degrees of freedom. In addition, when using most model selection criteria to choose the tuning parameter for nuclear norm penalization, it oftentimes suffices to entertain a finite number of candidates as opposed to a continuum of choices. Numerical examples are also presented to illustrate the practical implications of our results.
基金supported by the National Science Foundations (DMS0504783 DMS0604207)National Science Fund for Distinguished Young Scholars of China (70825005)
文摘This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.
文摘In this paper, we explore the properties of a positive-part Stein-like estimator which is a stochastically weighted convex combination of a fully correlated parameter model estimator and uncorrelated parameter model estimator in the Random Parameters Logit (RPL) model. The results of our Monte Carlo experiments show that the positive-part Stein-like estimator provides smaller MSE than the pretest estimator in the fully correlated RPL model. Both of them outperform the fully correlated RPL model estimator and provide more accurate information on the share of population putting a positive or negative value on the alternative attributes than the fully correlated RPL model estimates. The Monte Carlo mean estimates of direct elasticity with pretest and positive-part Stein-like estimators are closer to the true value and have smaller standard errors than those with fully correlated RPL model estimator.
基金Supported by the Aerospace Science and Technology Innovation Foundation of China (2006)
文摘An effective de-noising method for fiber optic gyroscopes （FOGs） is proposed. This method is based on second-generation Daubechies D4 （DB4） wavelet transform （WT） and level-dependent threshold estimator called Stein＇s unbiased risk estimator （SURE）. The whole approach consists of three critical parts： wavelet decomposition module, parameters estimation module and SURE de-noising module. First, DB4 wavelet is selected as lifting base of the second-generation wavelet in the decomposition module. Second, in the parameters estimation module, maximum likelihood estimation （MLE） is used for stochastic noise parameters estimation. Third, combined with soft threshold de-noising technique, the SURE de-noising module is designed. For comparison, both the traditional universal threshold wavelet and the second-generation Harr wavelet method are also investigated. The experiment results show that the computation cost is 40% less than that of the traditional wavelet method. The standard deviation of de-noised FOG signal is 0.012 and the three noise terms such as angle random walk, bias instability and quantization noise are reduced to 0.007 2°/√h, 0.004 1° / h, and 0.008 1°, respectively.
