对半参数回归模型yi=χiTβ+g(χi)+ei,i=1,2,…,n,对非参数函数g(·)采用核估计的方法,构造了参数向量β的L-估计量λn,在一些正则条件下,获得了λn的渐近正态性和非参数函数g(·)的估计量gn(t)的最优收敛速度可达到O(n-(1/3)),并且给出了标准化L估计量λn的渐近分布的Berry-Es界.

Consider a semi-parametric regression model Y = xTB + g(t) + e, The L-estimators n and g for B and g() are constructed. Under same natural and reasonable conditions, the asymptotic normality and Berry-Esseen bound for n is obtained. The best convergence rate of g_n(t) are showm to be 0(n~(-1\3)).