Double asymptotics for the chi-square statistic

作者：Rempala Grzegorz A^*; Wesolowski Jacek

来源：Statistics & Probability Letters, 2016, 119: 317-325.

DOI：10.1016/j.spl.2016.09.004

• Pearson chi-square statistic
• Central limit theorem
• Poisson limit theorem
• Weak convergence

We consider distributional limit of the Pearson chi-square statistic when the number of classes m(n) increases with the sample size n and n/root m(n) -> lambda. Under mild moment conditions, the limit is Gaussian for lambda = infinity, Poisson for finite lambda > 0, and degenerate for lambda = 0.

• 出版日期2016-12