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

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2022-02-01 DOI:10.1515/dma-2022-0003

M. P. Savelov

引用次数: 0

Abstract

Abstract 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.

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包含Pearson统计量的多项式格式中的一类渐近独立统计量

摘要我们考虑一个具有N个结果的多项式格式。Pearson统计量是检验结果概率由数字p1，…，pN给出的假设的经典统计量。我们提出了两个N−2统计量，它们与Pearson统计学一起构成了一组N−1渐近联合独立的随机变量，并找到了它们的极限分布。皮尔逊统计量是渐近正态随机向量长度的平方。建议的统计量是该向量在一些辅助球面坐标系中的坐标。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics and Applications MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

20.00%

发文量

期刊介绍： The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.