Consider the following heteroscedastic semiparametric regression model: y_i = Xi T β + g(ti) + σiei, 1 ≤ i ≤ n, where {Xi, 1 ≤ i ≤ n} are random design points, errors {ei, 1 ≤ i ≤ n} are negatively associated ...Consider the following heteroscedastic semiparametric regression model: y_i = Xi T β + g(ti) + σiei, 1 ≤ i ≤ n, where {Xi, 1 ≤ i ≤ n} are random design points, errors {ei, 1 ≤ i ≤ n} are negatively associated (NA) random variables, σi2 = h(ui), and {ui} and {ti} are two nonrandom sequences on [0, 1]. Some wavelet estimators of the parametric component β, the non- parametric component g(t) and the variance function h(u) are given. Under some general conditions, the strong convergence rate of these wavelet estimators is O(n^(-1/3) log n). Hence our results are extensions of those results on independent random error settings.展开更多
We study the properties of the Lasso in the high-dimensional partially linear model where the number of variables in the linear part can be greater than the sample size.We use truncated series expansion based on polyn...We study the properties of the Lasso in the high-dimensional partially linear model where the number of variables in the linear part can be greater than the sample size.We use truncated series expansion based on polynomial splines to approximate the nonparametric component in this model.Under a sparsity assumption on the regression coefficients of the linear component and some regularity conditions,we derive the oracle inequalities for the prediction risk and the estimation error.We also provide sufficient conditions under which the Lasso estimator is selection consistent for the variables in the linear part of the model.In addition,we derive the rate of convergence of the estimator of the nonparametric function.We conduct simulation studies to evaluate the finite sample performance of variable selection and nonparametric function estimation.展开更多
This paper considers a semi-varying coefficient model for panel data with fixed effects,proposes the profile-likelihood-based estimators for the parametric and nonparametric components,and establishes convergence rate...This paper considers a semi-varying coefficient model for panel data with fixed effects,proposes the profile-likelihood-based estimators for the parametric and nonparametric components,and establishes convergence rates and asymptotic normality properties for both estimators.Simulation results show that the proposed estimators behave well in finite sample cases.展开更多
基金supported by the National Natural Science Foundation of China (No. 11071022)the Key Project of the Ministry of Education of China (No. 209078)the Youth Project of Hubei Provincial Department of Education of China (No. Q20122202)
文摘Consider the following heteroscedastic semiparametric regression model: y_i = Xi T β + g(ti) + σiei, 1 ≤ i ≤ n, where {Xi, 1 ≤ i ≤ n} are random design points, errors {ei, 1 ≤ i ≤ n} are negatively associated (NA) random variables, σi2 = h(ui), and {ui} and {ti} are two nonrandom sequences on [0, 1]. Some wavelet estimators of the parametric component β, the non- parametric component g(t) and the variance function h(u) are given. Under some general conditions, the strong convergence rate of these wavelet estimators is O(n^(-1/3) log n). Hence our results are extensions of those results on independent random error settings.
文摘We study the properties of the Lasso in the high-dimensional partially linear model where the number of variables in the linear part can be greater than the sample size.We use truncated series expansion based on polynomial splines to approximate the nonparametric component in this model.Under a sparsity assumption on the regression coefficients of the linear component and some regularity conditions,we derive the oracle inequalities for the prediction risk and the estimation error.We also provide sufficient conditions under which the Lasso estimator is selection consistent for the variables in the linear part of the model.In addition,we derive the rate of convergence of the estimator of the nonparametric function.We conduct simulation studies to evaluate the finite sample performance of variable selection and nonparametric function estimation.
基金supported by the National Natural Science Foundation of China under Grant No.11101452the Natural Science Foundation Project of CQ CSTC under Grant No.2012jjA00035+2 种基金the National Basic Research Program of China under Grant No.2011CB808000the National Social Science Foundation of China under Grant No.12XTJ001the Natural Science Foundation Project of CTBU of China under Grant No.1352001
文摘This paper considers a semi-varying coefficient model for panel data with fixed effects,proposes the profile-likelihood-based estimators for the parametric and nonparametric components,and establishes convergence rates and asymptotic normality properties for both estimators.Simulation results show that the proposed estimators behave well in finite sample cases.
基金This research is supported by the National Natural Science Foundation of China under Grant No. 10771015 and the Start-Up Funds for Doctoral Scientific Research of Shandong University of Finance.
