Chi-square approximation by Stein's method with application to Pearson's statistic

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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.

Bibliographical metadata

Original languageEnglish
Pages (from-to)720-756
Number of pages37
JournalAnnals of Applied Probability
Issue number2
Early online date26 May 2017
StatePublished - 2017