Date of Award
Mathematics and Statistics
Fung, Karen (Mathematics & Statistics)
CC BY-NC-ND 4.0
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.
Ibrahim, Quazi, "Generalized Inference in Linear Regression Models" (2009). Electronic Theses and Dissertations. 351.