Geodesic
Chi-square type goodness of fit tests for composite hypothesis
Mathematica Applicanda, Tome 35 (2007) no. 49/08, pp. 109-125.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

Adapting the classical Pearson’s chi-square goodness-of-fit test for testing composite hypotheses brings serious problems with estimation of unknown parameters. An interesting solution which eliminates them was proposed by Dzhaparidze and Nikulin. The most important advantage of their solution is a possibility of using arbitrary estimators satisfying only a natural and weak condition. The aim of the present article is to popularize this solution. We provide a complete, short and, what is more elementary proof of the main theorem on asymptotic distribution of the test statistic. In addition, we prove that the constructed test belongs to a general class of score tests what advocates for its good properties. Finally, as an example, we give a typical implementation of the test to testing in location and scale family.
DOI : 10.14708/ma.v35i49/08.1390
Classification : 62F03
Mots-clés : Chi-square test, Composite hypothesis, n-square-consistent estimator, Dzhaparidze–Nikulina statistic, Score test. 
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Anita Małoń; Dagmara Ziółkowska. Chi-square type goodness of fit tests for composite hypothesis. Mathematica Applicanda, Tome 35 (2007) no. 49/08, pp.  109-125. doi : 10.14708/ma.v35i49/08.1390. http://geodesic.mathdoc.fr/articles/10.14708/ma.v35i49/08.1390/

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