CHI-SQUARE APPROXIMATION BY STEIN'S METHOD WITH APPLICATION TO PEARSON'S STATISTIC

• 成果类型: Article
• 署名作者: Gaunt, Robert E.; Pickett, Alastair M.; Reinert, Gesine
• 署名单位: University of Oxford
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1213
• 发表日期: 2017
• 页码: 720-756
• 关键词: convergence

摘要

This paper concerns the development of Stein's method for chi-square approximation and its application to problems in statistics. New bounds for the derivatives of the solution of the gamma Stein equation are obtained. These bounds involve both the shape parameter and the order of the derivative. Subsequently, Stein's method for chi-square approximation is applied to bound the distributional distance between Pearson's statistic and its limiting chi-square distribution, measured using smooth test functions. In combination with the use of symmetry arguments, Stein's method yields explicit bounds on this distributional distance of order n(-1).