固定设计点的半参数回归模型的M估计的渐进分布(英文)

Asymptotic Distributions of M-estimators of the Parametric Components of Partly Linear Models with Fixed Carriers

讨论了固定设计点的半参数回归模型的大样本性质，得到了模型的M估计的渐进分布，并建立了关于参数的检验．数值模拟结果表明，本文提出的方法具有较好的稳健性．

This paper deals with the problerns of M-estimators for the partly linear model where un are random errors, the (Ti, Xi)'s are known fixed carriers, Xi∈Rd, and Ti ∈ [0, 1], Yi is real-valued, i = 1, 2,''' ,n, β is a d-vector of parameters, and g0(.) is an unknown function. The proposed estimators of β and g0(t) in thi8 paper are β and gn(t)=(t)α respectively, where a and βminimize (.) is a vecor of the basis functions of a piecewise polynomial space and (.) is a function chosen suitably We consider testing the hypothesi8 H0: A'β0 =β. Under some regularity conditions it is shown that β is asytotically normal and the test statistic converges in distribution to a chi square distribution of degree of freedom d0, where ds is the dimension of β. The large-sample tests of linear hypotheses on β show satisfactory performance in our simulated example.