TY - JOUR

T1 - A family of asymptotically independent statistics in polynomial scheme containing the Pearson statistic

AU - Savelov, Maxim P.

N1 - Publisher Copyright: © 2022 Walter de Gruyter GmbH, Berlin/Boston.

PY - 2022/2/1

Y1 - 2022/2/1

N2 - We consider a polynomial scheme with N outcomes. The Pearson statistic is the classical one for testing the hypothesis that the probabilities of outcomes are given by the numbers p1,.., pN. We suggest a couple of N-2 statistics which along with the Pearson statistics constitute a set of N-1 asymptotically jointly independent random variables, and find their limit distributions. The Pearson statistics is the square of the length of asymptotically normal random vector. The suggested statistics are coordinates of this vector in some auxiliary spherical coordinate system.

AB - We consider a polynomial scheme with N outcomes. The Pearson statistic is the classical one for testing the hypothesis that the probabilities of outcomes are given by the numbers p1,.., pN. We suggest a couple of N-2 statistics which along with the Pearson statistics constitute a set of N-1 asymptotically jointly independent random variables, and find their limit distributions. The Pearson statistics is the square of the length of asymptotically normal random vector. The suggested statistics are coordinates of this vector in some auxiliary spherical coordinate system.

KW - angular statistics

KW - Chi-square test

KW - limit distributions

KW - Pearson statistics

UR - http://www.scopus.com/inward/record.url?scp=85126040604&partnerID=8YFLogxK

U2 - 10.1515/dma-2022-0003

DO - 10.1515/dma-2022-0003

M3 - Article

AN - SCOPUS:85126040604

VL - 32

SP - 39

EP - 45

JO - Discrete Mathematics and Applications

JF - Discrete Mathematics and Applications

SN - 0924-9265

IS - 1

ER -