题 目：A New Wald Test for Hypothesis Testing Based on MCMC outputs
主讲嘉宾：李 勇教授 中国人民大学
李勇，盘古智库学术委员、青年长江学者，中国人民大学汉青经济与金融高级研究院院长助理，香港中文大学博士，新加坡管理大学金融学博士后。在Journal of Econometrics, Journal of Future Market, Quantitative Finance等国内外优秀刊物上发表了近三十篇学术论文，其SSCI/SCI收录20篇，主持多项国家自然科学基金，省部级基金项目。曾获得教育部新世纪人才、北京市青年优秀人才称号。
In this paper, a new and convenient χ2 wald test based on MCMC outputs is proposed for hypothesis testing. The new statistic can be explained as MCMC version of Wald test and has several important advantages that make it very convenient in practical applications. First, it is well-defined under improper prior distributions and avoids Jeffrey-Lindley’s paradox. Second, it’s asymptotic distribution can be proved to follow the χ2 distribution so that the threshold values can be easily calibrated from this distribution. Third, it’s statistical error can be derived using the Markov chain Monte Carlo (MCMC) approach. Fourth, most importantly, it is only based on the posterior MCMC random samples drawn from the posterior distribution. Hence, it is only the by-product of the posterior outputs and very easy to compute. In addition, when the prior information is available, the finite sample theory is derived for the proposed test statistic. At last, the usefulness of the test is illustrated with several applications to latent variable models widely used in economics and finance.