NOTE ON DISTRIBUTION FREE TESTING FOR DISCRETE DISTRIBUTIONS
成果类型：
Article
署名作者：
Khmaladze, Estate
署名单位：
Victoria University Wellington
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/13-AOS1176
发表日期：
2013
页码：
2979-2993
关键词：
摘要：
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 = nu(in)-npi/root np(i,) i = l, ... , 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 Sigma(l <= 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.