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

考虑回归模型：ｙｉ＝ｘｉβ＋ｇ（ｔｉ）＋σｉｅｉ，１ｉｎ，其中σ２ｉ＝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，ｅｉ是随机误差．对文［１］给出的基于ｇ（·）及ｆ（·）的一类非参数估计的β的最小二乘估计＾βｎ和加权最小二乘估计βｎ，我们在适当条件下证明了它们的强相合性．

Consider the heteroscedastic regression model: y i=x iβ+g(t i)+σ ie i,1in , where σ 2 i=f(u i) . Here the design points (x i,t i,u i) are known and nonrandom, g and f are unknown functions, and e i is an unobserved disturbance. For the least squares estimator n and the weighted least squares estimator n of β given in based on the family of nonparametric estimates of g(·) and f(·) , we establish their strong consistency under suitable conditions.