Research On Several Classes Of Semiparametric And Parametric Models For Categorical Data

Categorical data in this paper refers to a series of(ordered or unordered)categories or some imprecise linguistic values.Categorical data exists in many fields such as sociology,economics and biomedicine.With the increasing demand for data analysis,statistical modeling of such data has important theoretical and practical significance.This paper focuses on the multicollinearity problem of logistic partial linear regression model under categorical data,the estimation problem of logistic partial linear regression model with mixed ordered and unordered categorical nuisance covariates,a class of mixed models of ordered categorical response and its estimation;And the definition,estimation and application of ARMA model for imprecise linguistic valued data under the membership function.(1)Based on the profile likelihood estimation,this paper proposes a generalized Liu-type estimation method to eliminate multicollinearity of the logistic partial linear regression model on the basis of ridge estimation,Liu estimation and Liu-type estimation.Under the asymptotic mean square error matrix(MSEM)criterion,the optimality condition of generalized Liu-type estimation is given.The optimal choices of the bias parameter and the bias parameter function in the generalized Liu-type estimator are given.Simulation experiments and empirical analysis are carried out.(2)The simplified categorical kernel function is applied to the logistic partial linear regression model with mixed categorical nuisance covariates,and the regression relationship between linear covariates and nuisance covariates is defined,and an improved iterative weighted least squares estimation algorithm is proposed.The simulation and empirical results of this method are given.(3)Starting from the response style supported by Zipf’s law,we propose a novel mixture model for ordered categorical responses via replacing the uncertainty component of the CUB model with a truncated Zeta distribution.The EM algorithm for parameter estimation of this model,the approximation of the truncated Riemannian Zeta function and the asymptotic variance-covariance matrix of the parameter estimators are given.The simulation and empirical results of the model are given.(4)Under the membership function method,the mean,variance,covariance,a standardized process of errors and ARMA model are defined by fuzzy random variables for imprecise linguistic valued data,and the least squares estimation as well as its asymptotic properties for this model under the distance L2 between sets are obtained.The simulation and empirical results of this model are given.