On goodness-of-fit tests for lattice distributions. (English) Zbl 0935.62053

Conti, Pier Luigi

Theory Probab. Math. Stat. 57, 85-99 (1998) and Teor. Jmovirn. Mat. Stat. 57, 81-95 (1997).

During the last years goodness-of-fit tests for lattice distributions have received considerable attention. A common tool, widely used in the statistical literature, is the empirical probability generating function (p.g.f.). The main alternative to goodness-of-fit tests based on the empirical p.g.f. are apparently chi-square type tests. However, the classical chi-square test and its modifications are based on a finite number of classes.
The basic idea of this paper consists in letting the number of classes tend to infinity when the sample size goes to infinity. It is shown that a consistent test is obtained. The main contribution of the present paper is the construction of a consistent and asymptotically normal chi-square test of goodness-of-fit for general discrete distributions. It is also proved that similar results hold for the family of power-divergence statistics.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

62G10	Nonparametric hypothesis testing
62G20	Asymptotic properties of nonparametric inference
62F05	Asymptotic properties of parametric tests

Keywords:

goodness-of-fit tests; lattice distributions