Accession Number : ADA186712
Title : Variance Function Estimation. Revision.
Descriptive Note : Journal article Aug 86-Aug 87,
Corporate Author : NORTH CAROLINA UNIV AT CHAPEL HILL INST OF STATISTICS
Personal Author(s) : Davidian, Marie ; Carroll, R J
Report Date : Mar 1987
Pagination or Media Count : 52
Abstract : Heteroscedastic regression models are used in fields including economics, engineering, and the biological and physical sciences. This paper studies variance function estimation in a unified way, focusing on common methods proposed in the statistical and other literature, in order to make both general observations and compare different estimation schemes. There are significant differences in both efficiency and robustness for many common methods. A general theory is developed for variance function estimation, focusing on estimation of the structural parameters and including most methods in common use in our development. The general qualitative conclusions are these. First, most variance function estimation procedures can be looked upon as regressions with responses being transformations of absolute residuals from a preliminary fit or sample standard deviations from replicates at a design point. The former is typically more efficient, but not uniformly so. Secondly, for variance function estimates based on transformations of absolute residuals, we show that efficiency is a monotone function of the efficiency of the fit from which the residuals are formed, at least for symmetric errors. Our conclusion is that one should iterate so that residuals are based on generalized least squares. Finally, robustness issues are of even more importance here than in estimation of a regression function for the mean. The loss of efficiency of the standard method away from the normal distribution is much more rapid than in the regression problem.
Descriptors : *REGRESSION ANALYSIS , RESIDUALS , MONOTONE FUNCTIONS , ESTIMATES , LEAST SQUARES METHOD , NORMAL DISTRIBUTION , COVARIANCE , ASYMPTOTIC SERIES , TRANSFORMATIONS(MATHEMATICS) , PARAMETERS , RESIDUALS , VARIATIONS , SYMMETRY
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE