Consider a semiparametric regression model with linear time series errors Yk=x'kβ+g(tk)+εk,1≤k≤n,where Yk's are responses,xk=(xk1，xk2，…,xkp)' and tk∈T包含R are fixed design points,β=(β1,β2,…,β...Consider a semiparametric regression model with linear time series errors Yk=x'kβ+g(tk)+εk,1≤k≤n,where Yk's are responses,xk=(xk1，xk2，…,xkp)' and tk∈T包含R are fixed design points,β=(β1,β2,…,βp)'is an unknown parameter vector,g(·)is an unknonwn bounded real-valued function defined on a compact subset T of the real line R,and εk is a linear process given by εk=∑j=0^∞ψjek-j,ψ0=1,where ∑j=0^∞|ψj|<∞,and ej,j=0,±1,±2,…,are i.i.d.random variables.In this paper we establish the asymptotic normality of the least squares estimator of β,a smooth estimator of g(·),and estimators of the autocovariance and autocorrelation functions of the linear process εk.展开更多
基金CHEN Min's work is supported by Grant No. 70221001 and No. 70331001 from NNSFC and Grant No. KZCX2-SW-118 from CAS.
文摘Consider a semiparametric regression model with linear time series errors Yk=x'kβ+g(tk)+εk,1≤k≤n,where Yk's are responses,xk=(xk1，xk2，…,xkp)' and tk∈T包含R are fixed design points,β=(β1,β2,…,βp)'is an unknown parameter vector,g(·)is an unknonwn bounded real-valued function defined on a compact subset T of the real line R,and εk is a linear process given by εk=∑j=0^∞ψjek-j,ψ0=1,where ∑j=0^∞|ψj|<∞,and ej,j=0,±1,±2,…,are i.i.d.random variables.In this paper we establish the asymptotic normality of the least squares estimator of β,a smooth estimator of g(·),and estimators of the autocovariance and autocorrelation functions of the linear process εk.
