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（ｘｉ）＋σｉｅｉ，１≤ｉ≤ｎ，其中σｉ２＝ｆ（ｕｉ），（ｘｉ，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是随机干扰．本文基于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，在适当的条件下证明了它们的强相合性．

Consider the heteroscedastic regression model; y i=x iβ+g(x i)+σ ie i,1≤i≤n ,where σ i 2=f(u i) ,Here the design points ( x i,u i )are known and nonrandom, g (·) and f (·) are unknown functions, β is unknown parametric,and e i is an unobserved disturbance.For the least squares estimator β and the weighted leasted squares estimator β n of β based on the family of honparametric estimates of g (·) and f (·), Their strong consistency under suitable conditions is established.