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A family of power‐divergence diagnostics for goodness‐of‐fit
Author(s) -
Carota Cinzia
Publication year - 2007
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.5550350406
Subject(s) - goodness of fit , dirichlet process , divergence (linguistics) , context (archaeology) , dirichlet distribution , multinomial distribution , mathematics , nonparametric statistics , bayesian probability , econometrics , statistics , geography , mathematical analysis , philosophy , linguistics , archaeology , boundary value problem
The author extends to the Bayesian nonparametric context the multinomial goodness‐of‐fit tests due to Cressie & Read (1984). Her approach is suitable when the model of interest is a discrete distribution. She provides an explicit form for the tests, which are based on power‐divergence measures between a prior Dirichlet process that is highly concentrated around the model of interest and the corresponding posterior Dirichlet process. In addition to providing interesting special cases and useful approximations, she discusses calibration and the choice of test through examples.