Statistical Inference For Varying Coefficient Partial Linear Models With Missing Censored Indicators

Censored data is widely used in finance,biology,medicine,engineering and other fields.Statistical modeling of censored data has always been a hot topic for scholars.This paper studies a special type of censored data model,which is a partial linear model of variable coefficients when the censored indicator is missing.First of all,what we have to solve is the problem of missing the missing indicator.Referring to the methods in the existing literature,we replace the missing part with an expected value.Secondly,for the non-parametric part,the difficulty of calculating the local polynomial method is overcome.We use the B-spline approximation;finally,we consider the combined quantile regression of the model,and statistically infer the parameters and non-parametric parts.The specific conclusions are as follows:Firstly,we consider the combined combination quantile regression of partial linear models,and obtain the asymptotic normality of the parameter estimation and the convergence speed of the non-parametric estimation.We used Monte Carlo simulation to verify the effectiveness of the proposed method,and applied this method to the comparison of tamoxifen and placebo in female breast cancer patients,and obtained the conclusions consistent with the actual survey results.Secondly,on the basis of the previous research,we studied the model variable selection problem.Based on the LASSO penalty,the variable selection of the parameter part was realized,and the large sample nature of the corresponding parameters was obtained.We validate the model using the Monte Carlo method and the results show that the proposed method is effective.We used this model in another data set on prostate cancer and got practical results.