Theory of probability and Mathematical statistics

Statistical sequential hypotheses testing on parameters of probability distributions of random binary data

A. J. Kharin

Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

Abstract: An important mathematical problem of computer data analysis – the problem of statistical sequential testing of simple hypotheses on parameters of probability distributions of observed binary data – is considered in the paper. This problem is being solved for two models of observation: for independent observations and for homogeneous Markov chains. Explicit expressions of the sequential tests statistics are derived, transparent for interpretation and convenient for computer realisation. An approach is developed to calculate the performance characteristics – error probabilities and mathematical expectations of the random number of observations required to guarantee the requested accuracy for decision rules. Asymptotic expansions for the mentioned performance characteristics are constructed under «contamination» of the probability distributions of observed data.

Keywords: random binary data; simple hypotheses; statistical sequential test; error probability; mathematical expectation of the random number of observations; «contamination»; asymptotic expansions.

UDC: 519.2

Language: English

DOI: 10.33581/2520-6508-2021-2-60-66