Double asymptotics for the chi-square statistic

Grzegorz A. Rempała and Jacek Wesołowski

Statistics & Probability Letters, 2016, vol. 119, issue C, 317-325

Abstract: We consider distributional limit of the Pearson chi-square statistic when the number of classes mn increases with the sample size n and n/mn→λ. Under mild moment conditions, the limit is Gaussian for λ=∞, Poisson for finite λ>0, and degenerate for λ=0.

Keywords: Pearson chi-square statistic; Central limit theorem; Poisson limit theorem; Weak convergence (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:119:y:2016:i:c:p:317-325

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DOI: 10.1016/j.spl.2016.09.004

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