title: Double asymptotics for the chi-square statistic.
abstract: Consider distributional limit of the Pearson chi-square statistic when the number of classesmnincreases with the sample sizenand [Formula: see text]. Under mild moment conditions, the limit is Gaussian forλ= ∞, Poisson for finiteλ> 0, and degenerate forλ= 0.
authors.affiliation: Division of Biostatistics and Mathematical Biosciences Institute, The Ohio State University, 43210 Columbus, OH USA.
authors.forename: Grzegorz A
authors.initials: GA
authors.lastname: Rempała
authors.affiliation: Wydział Matematyki i Nauk Informacyjnych, Politechnika Warszawska, Warsaw, Poland.
authors.forename: Jacek
authors.initials: J
authors.lastname: Wesołowski
keywords: Pearson chi-square statistic; Poisson limit theorem; central limit theorem; weak convergence