A Posterior-Based Wald-Type Statistic for Hypothesis Testing

 浙江大学数学科学学院九十周年院庆系列活动之四

题目：A Posterior-Based Wald-Type Statistic for Hypothesis Testing

时间：6月6日（周三）上午10:00―11:00

地点：工商楼2楼报告厅（200-9）

报告人：李勇教授（中国人民大学）

摘要：A new Wald-type statistic is proposed for hypothesis testing based on Bayesian posterior distributions. The new statistic can be explained as a posterior version of Wald test and have several nice properties. First, it is well-de_ned under improper prior distributions. Second, it avoids Jeffreys-Lindley's paradox. Third, under the null hypothesis and repeated sampling, it follows a _2 distribution asymptotically, offering an asymptotically pivotal test. Fourth, it only requires inverting the posterior covariance for the parameters of interest. Fifth and perhaps most importantly, when a

random sample from the posterior distribution (such as an MCMC output) is available, the proposed statistic can be easily obtained as a by-product of posterior simulation. In addition, the numerical standard error of the estimated proposed statistic can be computed based on the random sample. The finite sample performance of the statistic is examined in Monte Carlo studies. The method is applied to two latent variable models used in microeconometrics and financial econometrics.

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联系人：张荣茂教授（rmzhang@zju.edu.cn)