NA样本下部分线性模型中估计的强相合性

Strong Consistency of a Class of Estimators in Partial Linear Model for Negative Associated Samples

考虑回归模型：ｙｉ＝ｘｉβ＋ｇ（ｔｉ）＋σｉｅｉ，１＜ｉ＜ｎ，其中σ_ｉ～２＝ｆ（ｕｉ），（ｘｉ，ｔｉ，ｕｉ）是固定非随机设计点列，ｆ（·）和ｇ（·）是未知函数，β是待估参数，误差｛ｅｉ｝为ＮＡ变量．我们对β的最小二乘估计βｎ和加权最小二乘估计Ｂｎ，在适当的条件下得到了它们的强相合性．

Consider the heteroscedastic regression model: yi=xiβb+g(ti)+σiei, 1< i<n, where σ_i^2=f(ui)$. Here the design points (xi,ti,ui) are known and nonrandom, g and f are unknown functions, β is an unknown parameter to be estimated, and the errors {ei} are negatively associated random variables. For the least squares estimator βn and the weighted least squares estimator βn of β, we establish their strong consistency under suitable conditions.