误差为鞅差序列的部分线性模型中估计的强相合性

考虑回归模型:y_i=x_{i ^β} +g(ti)+σ_ie_i ,i=1,2,...,n,其中 σ_i=f(u_i), (x_i,t_i,u_i)是固定非随机设计点列,f(^.),\ g(^.)$\ 是未知函数,β是待估参数,e_i是随机误差且关于非降σ -代数列{F_i,i≥1} 为鞅差序列.对文献1]给出的基于f^(.)及g(^.)的一类非参数估计的β的最小二乘估计β_n和加权最小二乘估计β_n,在适当条件下证明了它们的强相合性,推广了文献6]在e_i为iid情形下的结果.

Strong Consistency of a Class of Estimators in Partial LinearModel under Martingale Difference Sequence

Consider the heteroscedastic regression model: y_i=x_{i ^β} +g(ti)+σ_ie_i ,i=1,2,...,n,where Here σ_i=f(u_i), (x_i,t_i,u_i)Here the design points (x_it_i,u_i) are known and nonrandom, g and ^_f are unknown functions , and β is the parameter needed to be estimated,e_i is the random error and a martingale difference sequence in relation to the undecreasing σ-algebra series {F_i,i≥1}. For the least squares estimator βn and the weighted least squares estimator βn of β given in 1] based on the family of nonparametric estimates of g(^.) and f^_(.), the authors establish their strong consistency under suitable conditions, thereby improve the the result where e_i is iid in 6].