Using Data Compressors to Construct Rank TestsReport as inadecuate

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* Corresponding author 1 SEQUEL - Sequential Learning LIFL - Laboratoire d-Informatique Fondamentale de Lille, Inria Lille - Nord Europe, LAGIS - Laboratoire d-Automatique, Génie Informatique et Signal 2 IDSIA - Istituto Dalle Molle di Studi sull-Intelligenza Artificiale

Abstract : Nonparametric rank tests for homogeneity and component independence are proposed, which are based on data compressors. For homogeneity testing the idea is to compress the binary string obtained by ordering the two joint samples and writing 0 if the element is from the first sample and 1 if it is from the second sample and breaking ties by randomization extension to the case of multiple samples is straightforward. $H 0$ should be rejected if the string is compressed to a certain degree and accepted otherwise. We show that such a test obtained from an ideal data compressor is valid against all alternatives. Component independence is reduced to homogeneity testing by constructing two samples, one of which is the first half of the original and the other is the second half with one of the components randomly permuted.

Keywords : data compressors Kolmogorov complexity component independence homogeneity testing information theory nonparametric statistical tests distribution-free statistical tests

Author: Daniil Ryabko - Juergen Schmidhuber -



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