REGRESSION ANALYSIS WITH SELECTION BIASED DEPENDENT VARIABLE (TRUNCATED DATA, STRATIFIED SAMPLES, CENSORED, KAPLAN-MEIR ESTIMATE, SEMI-PARAMETRIC MODEL

Regression analysis is widely used to study survey data in situa- tions where complex sampling designs are employed. Standard regression techniques can be applied when the data selection procedure is based on independent variables. However, the litera- ture abounds with examples where the selection procedure is based on or is related to the value of the dependent variable. Most of the current approaches are based on fully parametric assumptions regarding the regression model. The advantage of adopting a fully parametric regression model is that one can use maximum likelihood procedures to estimate the regression parameters under appropriate regularity conditions; the disadvantage is that one is restricted to an inflexible model. In this thesis, a semi-parametric regression model is studied, and we consider three qualitatively different situations under which observations are observed: (A) the probability of selection varies smoothly with the values of the dependent variable; (B) the stratified regression model: the population is stratified into several strata according to the value of dependent variable; the probabilities of selection are constant within strata but may vary across strata; (C) the truncated regression model: data can not be observed if the dependent variable value exceeds a certain limit. When the above situations occur, standard least square regression techniques can not be applied. The goal of this thesis is to provide estimates for the.;regression parameters and the residual distributions along with their large sample properties under situations (A), (B) and (C).;This research was supported in part by National Science Foundation Grants CEE 79-01642 and MCS 83-01257.