Some results in nonleast squares regression analysis

This thesis considers the regression analysis problem in which the estimators of the parameters are selected according to some criterion other than least squares. Two basic areas are considered. First, some basic properties are derived for the estimators that minimize the sum of the absolute values of the residuals raised to the X power. Both the homoscedastic and heteroscedastic cases are considered. Second, procedures for estimating weights for two types of heteroscedastic models are presented.