In this paper, we propose a new criterion, named PICa, to simultaneously select explanatory variables in the mean model and variance model in heteroscedastic linear models based on the model structure. We show that th...In this paper, we propose a new criterion, named PICa, to simultaneously select explanatory variables in the mean model and variance model in heteroscedastic linear models based on the model structure. We show that the new criterion can select the true mean model and a correct variance model with probability tending to 1 under mild conditions. Simulation studies and a real example are presented to evaluate the new criterion, and it turns out that the proposed approach performs well.展开更多
Wavelets are applied to detect the jumps in a heteroscedastic regression model. It is shown that the wavelet coefficients of the data have significantly large absolute values across fine scale levels near the jump poi...Wavelets are applied to detect the jumps in a heteroscedastic regression model. It is shown that the wavelet coefficients of the data have significantly large absolute values across fine scale levels near the jump points. Then a procedure is developed to estimate the jumps and jump heights. All estimators are proved to be consistent.展开更多
We reexamine the classical linear regression model when it is subject to two types of uncertainty:(i)some covariates are either missing or completely inaccessible,and(ii)the variance of the measurement error is undete...We reexamine the classical linear regression model when it is subject to two types of uncertainty:(i)some covariates are either missing or completely inaccessible,and(ii)the variance of the measurement error is undetermined and changing according to a mechanism unknown to the statistician.By following the recent theory of sublinear expectation,we propose to characterize such mean and variance uncertainty in the response variable by two specific nonlinear random variables,which encompass an infinite family of probability distributions for the response variable in the sense of(linear)classical probability theory.The approach enables a family of estimators under various loss functions for the regression parameter and the parameters related to model uncertainty.The consistency of the estimators is established under mild conditions in the data generation process.Three applications are introduced to assess the quality of the approach including a forecasting model for the S&P Index.展开更多
为准确计量与监测木荷生物量以及准确评估其碳汇能力、生态效益等生态功能,基于160株木荷样木实测数据,以胸径(D)、树高(H)、冠幅(Cw)和冠长(Cl)作为模型的自变量,运用非线性最小二乘法,采用15种模型结构建立木荷各组分生物量模型,并以1...为准确计量与监测木荷生物量以及准确评估其碳汇能力、生态效益等生态功能,基于160株木荷样木实测数据,以胸径(D)、树高(H)、冠幅(Cw)和冠长(Cl)作为模型的自变量,运用非线性最小二乘法,采用15种模型结构建立木荷各组分生物量模型,并以1/f(x)^2与1/f(x)^1.6分别作为权函数对模型进行异方差的消除,对比分析各模型拟合结果并选取各组分最优生物量模型。结果表明,木荷各部分的生物量模型采用同一模型结构所拟合的效果大致相同;各自变量对生物量模型的拟合效果与贡献程度从大到小顺序为D>H>Cl>Cw(其中自变量H与Cl的作用效果相近);随着函数模型的多元化,从一元到二元模型的提升效果明显,而后二元到多元模型提升效果不大,建议实际应用中采用二元模型W=a D b1 H b2即可;采用1/f(x)^1.6作为权函数消除异方差后模型整体的拟合效果与估计精度,优于未消除异方差与以1/f(x)^2作为权函数消除异方差的模型,证明以1/f(x)n作为通用权函数将更适用,但其具体n值需进一步研究。展开更多
The heteroscedastic regression model was established and the heteroscedastic regression analysis method was presented for mixed data composed of complete data,type-Ⅰ censored data and type-Ⅱ censored data from the l...The heteroscedastic regression model was established and the heteroscedastic regression analysis method was presented for mixed data composed of complete data,type-Ⅰ censored data and type-Ⅱ censored data from the location-scale distribution.The best unbiased estimations of regression coefficients,as well as the confidence limits of the location parameter and scale parameter were given.Furthermore,the point estimations and confidence limits of percentiles were obtained.Thus,the traditional multiple regression analysis method which is only suitable to the complete data from normal distribution can be extended to the cases of heteroscedastic mixed data and the location-scale distribution.So the presented method has a broad range of promising applications.展开更多
Consider a repeated measurement partially linear regression model with anunknown vector parameter β_1, an unknown function g(·), and unknown heteroscedastic errorvariances. In order to improve the semiparametric...Consider a repeated measurement partially linear regression model with anunknown vector parameter β_1, an unknown function g(·), and unknown heteroscedastic errorvariances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of ,we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that itimproves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given todetermine the number of iterations. We also show that when the number of replicates is less than orequal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of thosein [2] to the case of semiparametric regressions.展开更多
Consider the heteroscedastic regression model Yi = g（xi） ＋ σiei, 1 ≤ i ≤ n, where σi^2 = f（ui）, here （xi, ui） being fixed design points, g and f being unknown functions defined on [0, 1], ei being independe...Consider the heteroscedastic regression model Yi = g（xi） ＋ σiei, 1 ≤ i ≤ n, where σi^2 = f（ui）, here （xi, ui） being fixed design points, g and f being unknown functions defined on [0, 1], ei being independent random errors with mean zero. Assuming that Yi are censored randomly and the censored distribution function is known or unknown, we discuss the rates of strong uniformly convergence for wavelet estimators of g and f, respectively. Also, the asymptotic normality for the wavelet estimators of g is investigated.展开更多
In this paper, by making use of the Hadamard product of matrices, a natural and reasonable generalization of the univariate GARCH (Generalized Autoregressive Conditional heteroscedastic) process introduced by Bollersl...In this paper, by making use of the Hadamard product of matrices, a natural and reasonable generalization of the univariate GARCH (Generalized Autoregressive Conditional heteroscedastic) process introduced by Bollerslev (J. Econometrics 31(1986), 307-327) to the multivariate case is proposed. The conditions for the existence of strictly stationary and ergodic solutions and the existence of higher-order moments for this class of parametric models are derived.展开更多
We study the tail probability of the stationary distribution of nonparametric nonlinear autoregressive functional conditional heteroscedastic (NARFCH) model with heavytailed innovations. Our result shows that the tail...We study the tail probability of the stationary distribution of nonparametric nonlinear autoregressive functional conditional heteroscedastic (NARFCH) model with heavytailed innovations. Our result shows that the tail of the stationary marginal distribution of an NARFCH series is heavily dependent on its conditional variance. When the innovations are heavy-tailed, the tail of the stationary marginal distribution of the series will become heavier or thinner than that of its innovations. We give some specific formulas to show how the increment or decrement of tail heaviness depends on the assumption on the conditional variance function. Some examples are given.展开更多
Consider heteroscedastic regression model Yni= g（xni） ＋ σniεni （1 〈 i 〈 n）, where σ2ni= f（uni）, the design points （xni, uni） are known and nonrandom, g（.） and f（.） are unknown functions defined on cl...Consider heteroscedastic regression model Yni= g（xni） ＋ σniεni （1 〈 i 〈 n）, where σ2ni= f（uni）, the design points （xni, uni） are known and nonrandom, g（.） and f（.） are unknown functions defined on closed interval [0, 1], and the random errors （εni, 1 ≤i≤ n） axe assumed to have the same distribution as （ξi, 1 ≤ i ≤ n）, which is a stationary and a-mixing time series with Eξi =0. Under appropriate conditions, we study asymptotic normality of wavelet estimators of g（.） and f（.）. Finite sample behavior of the estimators is investigated via simulations, too.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10971007)Beijing Natural Science Fund (Grant No. 1072003)Science Fund of Beijing Education Committee
文摘In this paper, we propose a new criterion, named PICa, to simultaneously select explanatory variables in the mean model and variance model in heteroscedastic linear models based on the model structure. We show that the new criterion can select the true mean model and a correct variance model with probability tending to 1 under mild conditions. Simulation studies and a real example are presented to evaluate the new criterion, and it turns out that the proposed approach performs well.
文摘Wavelets are applied to detect the jumps in a heteroscedastic regression model. It is shown that the wavelet coefficients of the data have significantly large absolute values across fine scale levels near the jump points. Then a procedure is developed to estimate the jumps and jump heights. All estimators are proved to be consistent.
基金supported by the National Key R&D program of China(Grant Nos.2018YFA0703900 and ZR2019ZD41)the National Natural Science Foundation of China(Grant No.11701330)Taishan Scholar Talent Project Youth Project.
文摘We reexamine the classical linear regression model when it is subject to two types of uncertainty:(i)some covariates are either missing or completely inaccessible,and(ii)the variance of the measurement error is undetermined and changing according to a mechanism unknown to the statistician.By following the recent theory of sublinear expectation,we propose to characterize such mean and variance uncertainty in the response variable by two specific nonlinear random variables,which encompass an infinite family of probability distributions for the response variable in the sense of(linear)classical probability theory.The approach enables a family of estimators under various loss functions for the regression parameter and the parameters related to model uncertainty.The consistency of the estimators is established under mild conditions in the data generation process.Three applications are introduced to assess the quality of the approach including a forecasting model for the S&P Index.
文摘为准确计量与监测木荷生物量以及准确评估其碳汇能力、生态效益等生态功能,基于160株木荷样木实测数据,以胸径(D)、树高(H)、冠幅(Cw)和冠长(Cl)作为模型的自变量,运用非线性最小二乘法,采用15种模型结构建立木荷各组分生物量模型,并以1/f(x)^2与1/f(x)^1.6分别作为权函数对模型进行异方差的消除,对比分析各模型拟合结果并选取各组分最优生物量模型。结果表明,木荷各部分的生物量模型采用同一模型结构所拟合的效果大致相同;各自变量对生物量模型的拟合效果与贡献程度从大到小顺序为D>H>Cl>Cw(其中自变量H与Cl的作用效果相近);随着函数模型的多元化,从一元到二元模型的提升效果明显,而后二元到多元模型提升效果不大,建议实际应用中采用二元模型W=a D b1 H b2即可;采用1/f(x)^1.6作为权函数消除异方差后模型整体的拟合效果与估计精度,优于未消除异方差与以1/f(x)^2作为权函数消除异方差的模型,证明以1/f(x)n作为通用权函数将更适用,但其具体n值需进一步研究。
基金Supported by the National Natural Science Foundation of China(Grant No.10472006)
文摘The heteroscedastic regression model was established and the heteroscedastic regression analysis method was presented for mixed data composed of complete data,type-Ⅰ censored data and type-Ⅱ censored data from the location-scale distribution.The best unbiased estimations of regression coefficients,as well as the confidence limits of the location parameter and scale parameter were given.Furthermore,the point estimations and confidence limits of percentiles were obtained.Thus,the traditional multiple regression analysis method which is only suitable to the complete data from normal distribution can be extended to the cases of heteroscedastic mixed data and the location-scale distribution.So the presented method has a broad range of promising applications.
基金supported by a grant from the Natural Sciences and Engineering Research Council of Canada.
文摘Consider a repeated measurement partially linear regression model with anunknown vector parameter β_1, an unknown function g(·), and unknown heteroscedastic errorvariances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of ,we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that itimproves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given todetermine the number of iterations. We also show that when the number of replicates is less than orequal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of thosein [2] to the case of semiparametric regressions.
基金the National Natural Science Foundation of China(10571136)a Wonkwang University Grant in 2007
文摘Consider the heteroscedastic regression model Yi = g（xi） ＋ σiei, 1 ≤ i ≤ n, where σi^2 = f（ui）, here （xi, ui） being fixed design points, g and f being unknown functions defined on [0, 1], ei being independent random errors with mean zero. Assuming that Yi are censored randomly and the censored distribution function is known or unknown, we discuss the rates of strong uniformly convergence for wavelet estimators of g and f, respectively. Also, the asymptotic normality for the wavelet estimators of g is investigated.
文摘In this paper, by making use of the Hadamard product of matrices, a natural and reasonable generalization of the univariate GARCH (Generalized Autoregressive Conditional heteroscedastic) process introduced by Bollerslev (J. Econometrics 31(1986), 307-327) to the multivariate case is proposed. The conditions for the existence of strictly stationary and ergodic solutions and the existence of higher-order moments for this class of parametric models are derived.
基金supported by the National Natural Science Foundation of China(Grant No.10471005).
文摘We study the tail probability of the stationary distribution of nonparametric nonlinear autoregressive functional conditional heteroscedastic (NARFCH) model with heavytailed innovations. Our result shows that the tail of the stationary marginal distribution of an NARFCH series is heavily dependent on its conditional variance. When the innovations are heavy-tailed, the tail of the stationary marginal distribution of the series will become heavier or thinner than that of its innovations. We give some specific formulas to show how the increment or decrement of tail heaviness depends on the assumption on the conditional variance function. Some examples are given.
基金supported by the National Natural Science Foundation of China under Grant No.10871146the Grant MTM2008-03129 from the Spanish Ministry of Science and Innovation
文摘Consider heteroscedastic regression model Yni= g（xni） ＋ σniεni （1 〈 i 〈 n）, where σ2ni= f（uni）, the design points （xni, uni） are known and nonrandom, g（.） and f（.） are unknown functions defined on closed interval [0, 1], and the random errors （εni, 1 ≤i≤ n） axe assumed to have the same distribution as （ξi, 1 ≤ i ≤ n）, which is a stationary and a-mixing time series with Eξi =0. Under appropriate conditions, we study asymptotic normality of wavelet estimators of g（.） and f（.）. Finite sample behavior of the estimators is investigated via simulations, too.
