ИСТИНА

Chi-square test based on the Pearson statistics is used to check whether frequencies of outcomes correspond to their hypothetical probabilities. A sequential version of this test is based on several Pearson statistics computed for nested samples; this version was considered in several papers. Here we show that nite-dimensional distributions of the process generated by values of Pearson statistics for a sequence of nested samples converge to nite-dimensional distributions of the specic stationary stochastic process - normalised Bessel process. This fact together with formulas for the limiting joint distributions of the Pearson statistics allow us to derive formulas for the density of nite-dimensional distributions of the Bessel process and asymptotic relations between error probabilities of usual and sequential tests based on the Pearson statistics.