Divergence-based tests for model diagnostic

Pearson’s χ 2 test, and more generally, divergence-based tests of goodness-of-fit are asymptotically χ 2 -distributed with m − 1 degrees of freedom if the numbers of cells m is fixed, the observations are i.i.d and the cell probabilities and model parameters are completely specified. Jiang [Jiang, J...

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Bibliographic Details
Published in:Statistics & probability letters 2008-09, Vol.78 (13), p.1702-1710
Main Authors: Esteban, M.D., Hobza, T., Morales, D., Marhuenda, Y.
Format: Article
Language:English
Subjects:
Distribution theory
Exact sciences and technology
General topics
Mathematics
Parametric inference
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
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Summary:Pearson’s χ 2 test, and more generally, divergence-based tests of goodness-of-fit are asymptotically χ 2 -distributed with m − 1 degrees of freedom if the numbers of cells m is fixed, the observations are i.i.d and the cell probabilities and model parameters are completely specified. Jiang [Jiang, J., 2001. A nonstandard χ 2 -test with application to generalized linear model diagnostics. Statistics and Probability Letters 53, 101–109] proposed a nonstandard χ 2 test to check distributional assumptions for the case of observations not identically distributed. Under the same setup, in this paper a family of divergence-based tests are introduced and their asymptotic distributions are derived. In addition 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.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2008.01.007