中文摘要：

考虑回归模型： yi=xiβ＋g（ti）＋σiei,i=1,2,…,n,其中σi=f（ui）,（xi,ti,ui）是固定非随机设计点列, f（·）,g（·）是未知函数,β是待估参数,ei是随机误差且关于非降σ-代数列{Fi,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ei为iid情形下的结果.

英文摘要：

　Consider the heteroscedastic： regression model： yi = xiβ＋g（ti）＋σiei,j= 1,2,…, n, whereσi = f（ui）. Here the design points （xi,ti,ui） are known and nonrandom, g and f are unknown functions , andβis the parameter needed to be estimated, e i is the random error and a martingale difference sequence in relation to the undecreasingσ-algebra series {Fi, i.≥1}. For the least squares estimatorβ^-nand the weighted least squares estimatorβ^-nofβgiven in [1] based on the family of nonparametric estimates of y（·） and f（·）, the authors establish their strong consistency under suitable conditions, thereby improve the the result where ei is iid in [6].