Statistical Inference On Semiparametric Model With Measurement Errors

The statistical research of the data with measurement errors have been one of the important problems in statistical research in the recent 20 years. If we ignore the error, the result would tend to be biased or even not consistent. Therefore, we must use the corresponding measurement error model to deal with the real problem. The statistical analysis of the data with measurement error is developing quickly. In this article, we studied the two models contained measurement error, the first one is the partially linear single index measurement error model. The other one is the semiparametric mixed cure model with long-term survivors data. In many biological medicine studies showed that some patients after treatment will not occur recurrence or death, which are considered as cured people. Obviously, We can not apply the traditional statistical analysis method. This article studied the model, the proportional hazards regression was used to simulate the survival time function, the logistic regression was used to simulate the rate of the cured part. The EM algorithm was used to estimate the Parameter.The contents of this paper are arranged as follows:the first part introduced some of the relevant basic knowledge; The second part describes the partial linear single index measurement error model, gives the method to estimate and illustrates the estimation performance with Monte Carlo simulation results; The third Part describes the semiparametric mixed cure model with measurement error, gives a method to estimate, and illustrates the estimation performance with Monte Carlo simulation results; we also evaluate the proposed method by the BMT data;The fourth part ends the paper with a brief summarize.