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A. P. Baranov, Yu. A. Baranov

A power divergence test in the problem of sample homogeneity for large numbers of outcomes and trials

In order to test homogeneity of r independent polynomial schemes with the same number of outcomes N under non-classical conditions where the numbers of trials n_d , d = 1, . . . , r, in each of the schemes and the number of outcomes N tend to infinity, we suggest a statistic I(λ, r) which is a multidimensional analogue of the statistic I(λ) introduced by T. Read and N. Cressie. We obtain conditions of asymptotic normality of the distributions of the statistics I(λ) and I(λ, r) for an arbitrary fixed integer λ, λ ≠ 0, −1, as N → ∞, n_dN ⁻¹ → ∞, d = 1, . . . , r. The expressions for the centring and normalising parameters are given in the explicit form for the hypothesis H₀ under which the distributions in these r schemes coincide, and for some class of alternatives close to H₀.

Discrete Mathematics and Applications, Walter de Gruyter

Print ISSN: 0924-9266
Volume: 15, 05/2005
Pages: 211 - 240

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