Jornal article

Hobza T., Esteban M., Morales D., Marhuenda Y.

Statistics & Probability Letters

2008

13 (2008)

1702-1710

0167-7152

Ing. Tomáš Hobza, Ph.D. (ÚTIA - Oddělení stochastické informatiky)

goodness of fit, devergence statistics, GLM, model checking,

Pearson's x2 test, and more generally, divergence-based tests of goodness-of-fit are asymptotically x2-distributed with m-1 degrees of freedom if the numbers of cells m is fixed, the observations are iid and the cell probabilities and model parameters are completely specified. Jiang (2001) proposed a nonstandard x2 test to check distributional assumptions for the case of observations not identically distributed. Under the same set up, in this paper a family of divergence-based tests are introduced and their asymptotic distributions are derived. In additions bootstrap tests based on the given divergence test statistics are considered. Applications to generalized linear models diagnostic are proposed. A simulation study is carried out to investigate performance of several power divergence tests.