Robust Statistical Inference Of Two Different Data Types

In statistical research,we often need to deal with different types of data.First,Nonresponse is a very common phenomenon in survey sampling.Nonignorable nonresponse– that is,a response mechanism that depends on the values of the variable having nonresponse– is the most difficult type of nonresponse to handle.This dissertation develops a robust estimation approach to estimating equations(EEs)by incorporating the modelling of nonignorably missing data,the generalized method of moments(GMM)method and the imputation of EEs via the observed data rather than the imputed missing values when some responses are subject to nonignorably missingness.Based on a particular semiparametric logistic model for nonignorable missing response,this paper proposes the modified EEs to calculate the conditional expectation under nonignorably missing data.We apply the GMM to infer the parameters.The advantage of our method is that it replaces the non-parametric kernel-smoothing with a parametric sampling importance resampling(SIR)procedure to avoid nonparametric kernel-smoothing problems with high dimensional covariates.The proposed method is shown to be more robust than some current approaches by the simulations.In addition,regression model is an important tool to deal with spatial correlation data,which is widely used in the fields of spatial metrology,regional science and so on.Such as spatial autoregressive(SAR)model,the main research is the estimation of unknown coefficients in the regression model.In the past,most of the common regression analysis is based on the mean regression analysis,and some of the quantile regression analysis.Considering that the mean regression can not deal with the outliers and the asymmetric density function of variables well,this paper proposes a spatial autoregressive model based on mode regression.Mode has good robustness to outliers,and mode is more representative than mean in the case of asymmetric density function.Experiments were designed to analyze the effect of the model and verify the relevant conclusions.