误差为鞅差序列的部分线性模型中估计的渐近正态性

ASYMPTOTIC NORMALITY OF A CLASS OF ESTIMATORS IN PARTIAL LINEAR MODEL UNDER ERROR BEING MARTINGALE DIFFERENCE SEQUENCE

考虑回归模型yi=xiβ+g(ti)+ei,i=1,2,…,n,其中(xi,ti)是固定非随机设计点列,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,且满足E(e2n|Fn-1)-σ2=op(1),n→∞,其中0<2σ<∞为未知常数,本文基于g(.)的一类非参数估计的β的最小二乘估计■和2σ的估计量■,在适当条件下证明了其具有渐近正态性,从而推广了[1]在ei为iid情形下的结果.

The paper takes a regression model Yi=xiβ＋g（ti）＋ei,i=1,2,…,n into consideration. And according to a non-parametric estiomate based on g（.） and its least squares estimate fin , the paper proves its asymptotic normality. As a result, when ei equals lid, the result of [1] can be further developed. （ xi, ti） is fixed non-random-designed point matix, g（.） is unkown function,β is a parameter to be estimated, el is random error, the non-decreasing algebraic { Fi, i≥1 is martingale defference sequenece, and 0 〈 σ^2 〈∞ is unknown faction.