部分线性模型中L_1-估计量的渐近正态性(英文)

Asymptotic Normality of L_1-Estimators in a Partly Linear Model

给定部分线性模型Y=X′β0+g(t)+e,其中β0是一k×1未知参数向量,g(.)是一未知的光滑函数,e为一随机误差.我们先用一逐段多项式gn逼近未知函数g,然后用最小一乘法得到未知参数β0的最小绝对偏差估计量^β.在较弱的条件下我们推导了估计量^β的渐近正态性.

Consider the partly linear model Y=X＇β0 ＋g（T） ＋ e, where β0 is a k × 1 vector of unknown parameter, g（ · ） is an unknown smooth function and e is an unobserved disturbance. A piecewise polynomial gn （ · ） is proposed to approximate g and the least absolute deviation estimator of β0 is obtained. Under milder conditions the asymptotic distribution of the estimator of β0 is derived.