Studies Of Some Issues On Shrinkage Estimators In Censored Regression Model

Limited dependent variable (LDV) regression model is a virtual model and widely applied in many research fields, for example with econometrics, biomedicine and so on. In this paper, we study a special LDV model, saying the censored re-gression model, in which only response variable with values no less than0can be observed. Based on the censored regression model, we mainly focus on investigat-ing shrinkage estimation methods about parameters and group parameters, and using randomly weighting method to approximate to distribution of the proposed parameter estimates.Variable selection is one of the popular study issues during building statistical models. For the censored regression model, there is few references about variable selection. Motivated by the SCAD method in linear regression model, a SCAD-type shrinkage estimation method is proposed to choose effected explanatory vari-ables having contribution to model, and simultaneously provide an estimate of the corresponding coefficients. Under certain conditions, we obtain the sparsity prop-erty of estimate:zero coefficients can be estimated as0with probability tending to1, and build asymptotic distribution of estimate of non-zero coefficients. Simula-tion studies are conducted to illustrate the performance of the proposed shrinkage estimation method.Sometimes explanatory variables are expressed in group manner, for instance, in multifactor analysis of variance, categorical variable may be coded with a group of dummy variables. For the censored regression model, shrinkage estimate and variable selection methods, constructed with individual dummy variable, do not care about association between variables. To overcome this shortcoming, this paper proposes a group-type shrinkage estimate approach based on’pre-defined groups of variables. The approach can select the groups contributing to the cen-sored regression model, and simultaneously present an estimate of parameters in selected groups. Under some assumptions, sparsity and asymptotic distribution properties of estimates are obtained. In addition, we use some numerical studies and a real data example to demonstrate performance of our proposed method.In the rest of paper, we apply randomly weighting method to approximate the distribution of the proposed shrinkage estimation above-mentioned. Asymptotic distributions of the shrinkage estimates involve unknown nuisance parameters, for example with density function, which is difficult to be estimated, especially with small sample size. Randomly weighting method is employed to approximate distri-bution of the estimates without estimating nuisance parameters. We also obtain a randomly weighting estimate of parameter and a procedure of approximation is achieved. The approach directly provides variance estimate of the parameter estimate without estimating nuisance parameters, then it easily follows that statis-tical inference of the parameter estimate is formed. Finally, we build asymptotic properties of the the randomly weighting estimate, and numerical studies confirm the usefulness of the method.