Note on distribution free testing for discrete distributions

2014/01/03 by Estate Khmaladze · 2 citations
Mathematics · #math.ST #stat.TH

paper · pdf · doi:10.1214/13-aos1176

published as Annals of Statistics 2013, Vol. 41, No. 6, 2979-2993 · Published in at http://dx.doi.org/10.1214/13-AOS1176 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

arxiv created 2014/01/03 · arxiv updated 2014/01/06

Abstract

The paper proposes one-to-one transformation of the vector of components \Y_in\_i=1^m of Pearson's chi-square statistic, Y_in=\fracν_in-np_i√(np_i), i=1,…,m, into another vector \Z_in\_i=1^m, which, therefore, contains the same "statistical information," but is asymptotically distribution free. Hence any functional/test statistic based on \Z_in\_i=1^m is also asymptotically distribution free. Natural examples of such test statistics are traditional goodness-of-fit statistics from partial sums ∑_{I≤ k}Z_in. The supplement shows how the approach works in the problem of independent interest: the goodness-of-fit testing of power-law distribution with the Zipf law and the Karlin-Rouault law as particular alternatives.

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