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April 2017 Chi-square approximation by Stein’s method with application to Pearson’s statistic
Robert E. Gaunt, Alastair M. Pickett, Gesine Reinert
Ann. Appl. Probab. 27(2): 720-756 (April 2017). DOI: 10.1214/16-AAP1213


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 $n^{-1}$.


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Robert E. Gaunt. Alastair M. Pickett. Gesine Reinert. "Chi-square approximation by Stein’s method with application to Pearson’s statistic." Ann. Appl. Probab. 27 (2) 720 - 756, April 2017.


Received: 1 July 2015; Published: April 2017
First available in Project Euclid: 26 May 2017

zbMATH: 1370.60042
MathSciNet: MR3655852
Digital Object Identifier: 10.1214/16-AAP1213

Primary: 60F05, 62G10, 62G20

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.27 • No. 2 • April 2017
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