Date of Award
Doctor of Philosophy
Wayne A. Fuller
The problem of estimating the finite population distribution function of a variable y is studied. The framework is one in which auxiliary information is available for each element in the population, and is similar to the framework used by Chambers and Dunstan (1986). In this study we introduce a new estimator, called the local-residuals estimator, of the finite population distribution function with auxiliary information. The local-residuals estimator is based on the distribution of the residuals from the regression of the variable of interest, y, on the vector of auxiliary variables, x. One criticism of the estimator proposed by Chambers and Dunstan (1986) is that the performance of the estimator is poor when the superpopulation model is incorrectly specified. The local-residuals estimator is designed to be robust against model misspecification. The asymptotic properties of the local-residuals estimator are studied under different superpopulation models and the estimator is shown to be model consistent for the finite population distribution function. The conditions for asymptotic normality of the estimator are established and model consistent estimators of the variance of the local-residuals estimator are proposed. We also suggest an estimator of the superpopulation distribution function based on the local-residuals estimator. A Monte Carlo study compares the performance of the proposed estimator with alternative estimators presented in the literature.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Juan José Goyeneche
Goyeneche, Juan José, "Estimation of the distribution function using auxiliary information " (1999). Retrospective Theses and Dissertations. 12133.