On the absolute significance test for polynomial distribution

N. P. Salikhov

Essential Administration of Information Systems

Abstract: Upper estimates are found for the sum of probabilities of all the events $(x_1\ldots x_r)$, where $x_k$ is the frequency of the $k$th outcome in $n$ independent trials carried out according to a polynomial scheme of trials with $r$ possible outcomes, the probability of each of which does not exceed the probability of a fixed event observed in $n$ independent trials carried out according to the same scheme. Using these estimates we construct a test rejecting a polynomial scheme when the probabilities of outcomes in it are known.

Keywords: polynomial scheme of trials, absolute significance test, Kullback–Leibler distance, consistency of a test under a simple alternative, convex programming.

Received: 12.05.1996

DOI: 10.4213/tvp2182

 English version: Theory of Probability and its Applications, 1998, 42:4, 671–683

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