Publication at Faculty of Mathematics and Physics |
2010
Abstract
This paper aims to provide a partial literature review of goodness-of-fit tests with nuisance regression and scale parameters. For testing hypothesis of normality an extension of Shapiro-Wilk test is considered.
We describe two tests based on different approach for testing general hypothesis. The first one uses a comparison of a pair of scale estimators that are regression invariant and scale equivariant.
In the latter test nuisance parameters are estimated and the test statistics is based on a distance between the hypothetical characteristic function and the empirical characteristic function of residuals. A simulation study is performed to compare the power of these tests.