A power divergence test in the problem of sample homogeneity for large numbers of outcomes and trials
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A. P. Baranov
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 nd, 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 → ∞, ndN−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.
Copyright 2005, Walter de Gruyter
Articles in the same Issue
- A power divergence test in the problem of sample homogeneity for large numbers of outcomes and trials
- The Poisson approximation for the number of matches of values of a discrete function on segments of a sequence of random variables
- A theorem on probabilities of large deviations for decomposable statistics which do not satisfy the Cramér condition
- An upper bound for the number of functions satisfying the strict avalanche criterion
- Adjustment experiments for automata with variable logic of behaviour
- Equational closure
- Criteria for a Boolean function to be a repetition-free in the pre-elementary bases of rank 3
- On the length of checking test for repetition-free functions in the basis {0, 1, &, ∨, ¬}
- Touchard C-polynomials and quasi-orthogonal to them polynomials
Articles in the same Issue
- A power divergence test in the problem of sample homogeneity for large numbers of outcomes and trials
- The Poisson approximation for the number of matches of values of a discrete function on segments of a sequence of random variables
- A theorem on probabilities of large deviations for decomposable statistics which do not satisfy the Cramér condition
- An upper bound for the number of functions satisfying the strict avalanche criterion
- Adjustment experiments for automata with variable logic of behaviour
- Equational closure
- Criteria for a Boolean function to be a repetition-free in the pre-elementary bases of rank 3
- On the length of checking test for repetition-free functions in the basis {0, 1, &, ∨, ¬}
- Touchard C-polynomials and quasi-orthogonal to them polynomials
