Testing Serial Correlation In Semi-parametric Regression Model With Missing Data

In statistical analysis,the ideal case is that the collected data are completed.But in the real world,missing data is often inevitable,due to many reasons such as the differences of access to data and structural understanding of data,which caused that the collected data is incomplete and noisy.These missing data tend to have a negative impact on the statistical analysis.For example,they will affect the correctness of model and the accuracy of export rules intensively inferred from the data set,leading to a wrong model.Therefore,how to correctly handle missing data is extremely important.Semi-parametric regression model,with strong effectiveness and high robustness,was studied and applied more widely.Partial linear model and partial linear single index model are two classic models of it.There has been much work on the serial correlation test,but there has been tiny work about the testing serial correlation in regression model with missing data.This paper focuses on the serial correlation test of partially linear model with covariates missing and partially linear model single-index with response variables missing.Firstly,we impute the missing values of the data and construct the testing statistics.Then,under the null hypothesis,we estimate the unknown parametric and prove that the testing statistics has an asymptotic chi-square distribution.Finally,we use R to simulate our method,and simulation results indicate that our method performs well both in size and power.