污染数据半参数回归模型中的强相合估计

Strong Consistency Estimation in Semiparametric Regression Model for Contaminated Data

同删失数据一样 ,在实际工作中经常遇到一些关于污染数据的统计分析问题 .对于删失数据已得到了一系列较为深刻的结果 ,但对污染数据问题的研究却不多 .污染数据回归模型是生物统计中常用的模型 .考虑一类污染数据半参数回归模型 ,建立了模型的参数、回归函数和污染系数的估计 ,并在适当条件下证明了它们具有强相合性 .

As censored data,it often falls across some statistical analysis problems for contaminated data in actual work.There are a series of theories on censored data.However,there are not so many researches on problems for contaminated data.The regression model for contaminated data is a useful model in biostatistics.This paper considers a kind of semiparametric regression model for contaminated data.Under some suitable conditions it gives the estimators of parameter of the model,regression function and contaminated parameter.It is shown that they have strong consistency.