非齐次线性模型M估计的强相合性

摘要

研究非齐次线性模型M估计的强相合性.通过分析模型的统计性质,在比相关文献更弱的条件下,证明了非齐次线性模型M估计强相合的充分条件是δn=maxl≤i≤n(xi-(-x)n)′T-1n(xi-(-x)x)=O(n-δ),其中0＜δ＜1,并证明若要δ=1时结论依然成立须加强条件.本文结果比文献中的相应结果有所改进,文献结果可由本文结果导出.%The strong consistency of M estimator in inhomogeneous linear model was discussed. By analyzing the statistical property of inhomogeneous linear model, it is proved that under some weaker conditions the sufficient conditions of strong consistency of M estimators in inhomogeneous linear models is δm = ma x (xi—(x)n.)1Tn-1(x1 — (x)n) = O(n-a'). where 0<δ<1. When δ= 1, conditions must be strengthened to support the result. The corresponding theory of M estimators in inhomogeneous linear models can be inferenced from the results in this paper.