On some statistical properties of the “Book Stack” transformation

Abstract

This paper is devoted to the statistical properties of the so-called “Book Stack” transformation. It was proposed by B. Ryabko (Probl. Inf. Trans, 16(4), 1980) as the method of data compression. B. Ryabko and A. Pestunov used (Probl. Inf. Trans, 40(1), 2004) the transformation to construct the statistical test of the same name. The test is used to saying the null hypothesis that the “input” pure random sample is taken from the discrete uniform distribution with the given support. The idea of B. Ryabko and A. Pestunov is to verify this hypothesis with the help of the “output” sample which is obtained by the “Book Stack” transformation. Thus, arises the natural problem of comparing the results of the same criterion for “input” and “output” samples. Under the null hypothesis, procedures are equivalent, but if the null hypothesis fails, the results are generally different. Obviously, these results depend on the class of alternatives. The natural alternative is that the “input” pure random sample is taken from a discrete, but non-uniform, distribution with fixed support. We prove that several standard criteria applied to the “input” sample are more powerful than the same criteria applied to the “output” sample. In particular, this effect occurs for the likelihood ratio criterion and, with some formal restrictions, to the chi-square criterion. Refs 14.