Date of Award

2009

Degree Type

Thesis

Degree Name

M.Sc.

Department

Mathematics and Statistics

First Advisor

Fung, Karen (Mathematics & Statistics)

Keywords

Statistics, General.

Rights

CC BY-NC-ND 4.0

Abstract

In this thesis, we consider inference problems in linear regression under both homoscedasticity and heteroscedasticity of the error noise. Namely, we construct generalized confidence regions and generalized confidence intervals for regression coefficients of linear regression models. Regressor variables are considered non-stochastic. Independent normal errors with zero mean and constant or varying dispersion are considered. The regression data from two different regimes are considered. In testing the equality of the regression coefficients in the two regimes under heteroscedasticity, we develop the generalized pivotal quantities of their differences and the generalized p-values. Generalized methods of inference are especially useful in multiparameter cases where nontrivial tests are difficult to obtain. We propose generalized test variables and generalized p-values to test the equality of the sets of regression coefficients of the two regimes. The test can be applied efficiently for all sample sizes and for homoscedastic as well as heteroscedastic cases.

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