Contributions to the problem of goodness-of-fit

Abstract

<p>This dissertation consists of two parts. The first part pertains to residual goodness-of-fit analysis. The second part pertains to the possibility of bringing an asymptotic multi-decision point of view to goodness-of-fit analysis;Goodness-of-fit testing based on the Correlated (OLS) residuals for the standard linear regression model are investigated in the first part. A modification of the U-statistic is given and appropriate quantiles are discussed. Three new statistics for testing normality are introduced;Goodness-of-fit is also studied through orthogonally transformed residuals. Test size and power are studied for a new vector of transformed residuals (r*), as well as for Theil's BLUS residuals and comparisons are made with the result obtained for the OLS residuals;In the second part, the sense in which bivariate large deviations are pertinent to the three-decision view of goodness-of-fit is explored. Various approaches are discussed for computing or approximating the large deviation rates for the classification errors involved.</p>