In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity...In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity assumptions,some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process.In order to illustrate these results,some simulations such as con dence intervals and mean integrated square errors are provided in this paper.It shows that the residual density estimator can replace the density\estimator"which contains errors.展开更多
In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent(NSD, in short) random variables is established. By using the exponential inequality, we present some general ...In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent(NSD, in short) random variables is established. By using the exponential inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28]and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors.展开更多
The strong consistency of M estimator of regression parameter in linear model for φ-mixing samples is discussed by using the classic Rosenthal type inequality.We get the strong consistency of M estimator under lower ...The strong consistency of M estimator of regression parameter in linear model for φ-mixing samples is discussed by using the classic Rosenthal type inequality.We get the strong consistency of M estimator under lower moment condition,which generalizes and improves the corresponding ones for independent sequences.展开更多
基金supported by the National Natural Science Foundation of China(12131015,12071422)。
文摘In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity assumptions,some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process.In order to illustrate these results,some simulations such as con dence intervals and mean integrated square errors are provided in this paper.It shows that the residual density estimator can replace the density\estimator"which contains errors.
基金Supported by the National Natural Science Foundation of China(11501004,11501005,11526033,11671012)the Natural Science Foundation of Anhui Province(1508085J06,1608085QA02)+1 种基金the Key Projects for Academic Talent of Anhui Province(gxbj ZD2016005)the Research Teaching Model Curriculum of Anhui University(xjyjkc1407)
文摘In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent(NSD, in short) random variables is established. By using the exponential inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28]and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors.
基金Supported by the Anhui Provincial Natural Science Foundation（11040606M04） Supported by the National Natural Science Foundation of China（10871001,10971097）
基金The NSF (11201001,11171001,11126176) of Chinathe NSF (1208085QA03) of Anhui Province+2 种基金Provincial Natural Science Research Project (KJ2010A005) of Anhui CollegesDoctoral Research Start-up Funds Projects of Anhui Universitythe Students’ Innovative Training Project (2012003) of Anhui University
文摘The strong consistency of M estimator of regression parameter in linear model for φ-mixing samples is discussed by using the classic Rosenthal type inequality.We get the strong consistency of M estimator under lower moment condition,which generalizes and improves the corresponding ones for independent sequences.
