An empirical Bayes approach to variance function estimation

Abstract

The problem concerns the analysis of assay data when there have been previous similar experiments. Assay data usually fall under the framework of nonlinear regression when the variability about the regression line is non-constant, i.e. heteroscedastic. The typical model for assay data contains parameters β for the mean function and parameters θ for the variance function. Of interest are quantities such as the parameters themselves as well as nonlinear functions of them, e.g. the minimum detectable concentration. There are three basic ways in which such data have been analyzed: (a) take the means of the estimates of β and θ from all assays and use this as the estimate for the current assay; (b) use only the current assay to estimate β and θ and (c) use an empirical Bayes estimate. A small error asymptotic theory, in which all three methods are analyzed in a unified way, has been constructed and the empirical Bayes estimate has a non-normal limit distribution...