摘要
本文研究线性回归模型, Y=β'X+∈,并假设Y可被右删失,∈的分布函 数F0未知.本文证明,在某些条件下, β的一种改进的半参数极大似然法估计量β 有相合性. 同时证明,如果F0不连续,则P{β≠βi.o.}=0.这意味着以概率为一, 当样本很大时, β=β.文献中的现有估计量未见有关于这一性质的报道.相反,包括 Buckley-James估计量及M-估计量在内的大多数的估计量,都不满足这一性质.
Consider a linear regression model, Y =β'X + ∈, where Y may be right censored and the cdf F0 of ∈ is unknown. We show that a modified semi-parametric MLE, denoted by β, is strongly consistent under certain regularity conditions. Moreover, if F0 is discontinuous, then P(β≠βi.o.)=0, which means that P(β=β if the sample size is large)=1. The latter property has not been reported for the existing estimators. On the contrast, most estimators, such as the Buckley-James estimator and M-estimators β, satisfy that P(β≠βi.o.)=1.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2005年第2期391-396,共6页
Acta Mathematica Sinica：Chinese Series
