Robust estimation of the regression coefficients in complex surveys

Abstract

This thesis is concerned with the search for robust efficient procedures for estimating the regression coefficient in the marginal distribution of the survey variables for data collected from complex surveys. Parametric model based procedures which take into account the structure of the population by assuming a parametric model are found to be very sensitive to the violations of these underlying parametric model assumptions. However these procedures perform very well when the parametric model assumptions hold. Randomization based estimators, which takes into account the population structure through the selection probabilities, are found to be robust unconditionally but their conditional and efficiency properties may be poor in some circumstances. We propose nonparametric model based procedures which do not make any explicit assumptions about the distribution describing the population structure. One nonparametric procedure, namely the Nadaraya-Watson kernel estimator of the regression coefficient is the most efficient and robust when the structure of the population is unknown. However the estimator is biased when the population is linear and homoscedastic. The validity of the theoretical results was assessed in a series of simulation studies based on a variety of stratified sampling schemes.

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