Year: 1993
Type: dissertation
Abstract: Problem This dissertation is concerned w ith robust, rank based procedures in the heteroscedastic linear model.A frequent occurrence of such models is when the underlying scale (noise) is a function of the response (signal).For instance, the variance may be an increasing function of the mean of the response.Such models play havoc w ith the usual inference for linear models since homoscedasticity is a crucial assumption behind either classical or robust analysis of linear models.In this thesis we consider modeling this heteroscedasticity and robust estimation procedures of it.Using these scale estimation procedures, we obtain a complete robust analysis of the underlying linear model including estimation and confidence procedures for the regression coefficients.W e obtain asymptotic distribution theory for both our scale and linear model procedures.In order to compute our analysis, we have developed the necessary algorithms.W e also explore the small sample properties of our analysis w ith a M onte Carlo study.W e consider the heteroscedastic linear model (1.1) yi = x'ip + a id , i = l,---,1V, 1
Author: Sherry Dixon
Institution: Western Michigan University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2532338464