In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete co...In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete consistency result for the estimator of g(x) is presented.展开更多
We establish some results on the complete moment convergence for weighted sums of widely orthant-dependent(WOD)random variables,which improve and extend the corresponding results of Y.F.Wu,M.G.Zhai,and J.Y.Peng[J.Math...We establish some results on the complete moment convergence for weighted sums of widely orthant-dependent(WOD)random variables,which improve and extend the corresponding results of Y.F.Wu,M.G.Zhai,and J.Y.Peng[J.Math.Inequal.,2019,13(1):251–260].As an application of the main results,we investigate the complete consistency for the estimator in a nonparametric regression model based on WOD errors and provide some simulations to verify our theoretical results.展开更多
Consider the nonparametric regression model Y=go（T）+u,where Y is real-valued, u is a random error,T ranges over a nondegenerate compact interval,say[0,1],and go（·）is an unknown regression function,which is m...Consider the nonparametric regression model Y=go（T）+u,where Y is real-valued, u is a random error,T ranges over a nondegenerate compact interval,say[0,1],and go（·）is an unknown regression function,which is m（m≥0）times continuously differentiable and its ruth derivative,g<sub>0</sub><sup>（m）</sup>,satisfies a H■lder condition of order γ（m +γ】1/2）.A piecewise polynomial L<sub>1</sub>- norm estimator of go is proposed.Under some regularity conditions including that the random errors are independent but not necessarily have a common distribution,it is proved that the rates of convergence of the piecewise polynomial L<sub>1</sub>-norm estimator are o(n<sup>-2（m+γ）+1/m+γ-1/δ</sup>almost surely and o(n<sup>-2（m+γ）+1/m+γ-δ</sup>)in probability,which can arbitrarily approach the optimal rates of convergence for nonparametric regression,where δ is any number in （0, min（（m+γ-1/2）/3,γ））.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 exponen- tial inequality, we present some gen...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 exponen- tial 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
基金Supported by the Research Teaching Model Curriculum of Anhui University(xjyjkc1407)Supported by the Students Innovative Training Project of Anhui University(201310357004,201410357117,201410357249)Supported by the Quality Improvement Projects for Undergraduate Education of Anhui University(ZLTS2015035)
文摘In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete consistency result for the estimator of g(x) is presented.
基金China(Grant Nos.11671012,11871072)the Natural Science Foundation of Anhui Province(1808085QA03,1908085QA01,1908085QA07)+1 种基金the Provincial Natural Science Research Project of Anhui Colleges(KJ2019A0001,KJ2019A0003)the Students Innovative Training Project of Anhui University(S201910357342).
文摘We establish some results on the complete moment convergence for weighted sums of widely orthant-dependent(WOD)random variables,which improve and extend the corresponding results of Y.F.Wu,M.G.Zhai,and J.Y.Peng[J.Math.Inequal.,2019,13(1):251–260].As an application of the main results,we investigate the complete consistency for the estimator in a nonparametric regression model based on WOD errors and provide some simulations to verify our theoretical results.
基金Supported by the National Natural Science Foundation of China.
文摘Consider the nonparametric regression model Y=go（T）+u,where Y is real-valued, u is a random error,T ranges over a nondegenerate compact interval,say[0,1],and go（·）is an unknown regression function,which is m（m≥0）times continuously differentiable and its ruth derivative,g<sub>0</sub><sup>（m）</sup>,satisfies a H■lder condition of order γ（m +γ】1/2）.A piecewise polynomial L<sub>1</sub>- norm estimator of go is proposed.Under some regularity conditions including that the random errors are independent but not necessarily have a common distribution,it is proved that the rates of convergence of the piecewise polynomial L<sub>1</sub>-norm estimator are o(n<sup>-2（m+γ）+1/m+γ-1/δ</sup>almost surely and o(n<sup>-2（m+γ）+1/m+γ-δ</sup>)in probability,which can arbitrarily approach the optimal rates of convergence for nonparametric regression,where δ is any number in （0, min（（m+γ-1/2）/3,γ））.
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 exponen- tial 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.
