Statistical Inference For Clustered Data Under Missing-at-Random Mechanism

Under the background of the big data era,the structure and form of data become more complex and diverse.In addition to the common vertical data and time series data,the widely existing clustered data has also attracted the attention of statistical researchers.Clustered data structure is special,and due to various reasons,it is usually accompanied by missing.The existence of missing and the special structure and characteristics of clustered data make the research of clustered data complex.However,in the current research on clustered data,no scholars have considered the problem of missing,but in practice,ignoring the missing to study the cluster data is not reasonable.The statistical inference based on the missing clustered data has important theoretical and practical significance.The traditional statistical analysis methods can not adapt to the missing clustered data.There is an urgent need to popularize the traditional statistical analysis methods,so as to obtain more accurate and reasonable statistical analysis results when studying the missing clustered data.This paper considers the statistical inference of clustered data under missing-atrandom mechanism,and mainly studies the following two aspects: first,systematically study the estimation and statistical inference of linear regression model of clustered data under missing-at-random mechanism.A linear regression model is established for clustered data.Assuming that the data is randomly missing and the missing mechanism is a logistic regression model,the missing mechanism is estimated by iterative reweighted least square method,and it is proved that the parameter estimation in the missing mechanism is consistent; The inverse probability weighted least square method is used to estimate the parameters of the linear regression model of interest,and the consistency and asymptotic normality of the parameter estimation are proved; The 95 % confidence interval of inverse probability weighted least squares estimation of linear regression model is estimated by using Wild Cluster Bootstrap method.At the same time,the asymptotic effectiveness of Wild Cluster Bootstrap method for clustered data is proved theoretically; Finally,the simulation research and example analysis based on clustered data linear regression model are carried out.Secondly,the estimation and statistical inference of nonlinear regression model of clustered data under missing-at-random mechanism are systematically studied.A nonlinear regression model is established for clustered data.It is assumed that the data is randomly missing,and the assumption and estimation of the missing mechanism are the same as that of the linear regression model.The parameters of the nonlinear regression model of interest are estimated by using the inverse probability weighted least square method,and the consistency and asymptotic normality of the parameter estimation are proved; Finally,the simulation research and example analysis of nonlinear regression model based on clustered data are carried out.