统计与数据科学系系列学术报告之四百零三期

时    间：2023年7月10日（周一）10:00-11:00

主持人：复旦大学 管理学院 统计与数据科学系 郁文 教授

地    点：李达三楼104室

报告人：Cun-Hui Zhang  Distinguished Professor  Department of Statistics and Biostatistics，Rutgers University 

题    目：Chi-Squared and Normal Approximations in Large Contingency Tables

摘    要：We provide necessary and sucient conditions for the chi-squared and normal approximations of Pearson's chi-squared statistics for the test of independence and the goodness-of-fit test, as well as necessary and sufficient conditions for the normal approximation of the likelihood ratio and Hellinger statistics, when the cell probabilities of the multinomial data are in general pattern and the dimension diverges with the sample size. A cross-sample chi-squared statistic for testing independence applies to two-way contingency tables with diverging dimensions. A degrees-of-freedom adjusted chi-squared approximation applies continuously throughout the high-dimensional regime and matches Pearson's chi-squared statistic in both the mean and variance. Specific examples are provided to demonstrate the asymptotic normality of the three types of test statistics when the classical regularity conditions for the chi-squared and normal approximations are violated. Simulation results demonstrate that the chi-squared and normal approximations are more robust for the likelihood ratio and Hellinger statistics, compared with Pearson's chi-squared statistics. This talk is based on joint work with Chong Wu and Yisha Yao.

个人简介：张存惠教授是IMS和ASA的Fellow。其主要研究方向为： 高维数据 (High dimensional data)、经验Bayes (Empirical Bayes)、半参数与非参数方法（Semiparametric and Nonparametric Methods）、生存分析（Survival Analysis）、统计推断与概率论等。

 统计与数据科学系

2023-7-3