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Posterior-Based Wald-Type Statistic For Hypothesis Testing, Xiaobin Liu, Yong Li, Jun Yu, Tao Zeng
Posterior-Based Wald-Type Statistic For Hypothesis Testing, Xiaobin Liu, Yong Li, Jun Yu, Tao Zeng
Research Collection School Of Economics
A new Wald-type statistic is proposed for hypothesis testing based on Bayesian posterior distributions under the correct model specification. The new statistic can be explained as a posterior version of the Wald statistic and has several nice properties. First, it is well-defined under improper prior distributions. Second, it avoids Jeffreys–Lindley–Bartlett’s paradox. Third, under the null hypothesis and repeated sampling, it follows a distribution asymptotically, offering an asymptotically pivotal test. Fourth, it only requires inverting the posterior covariance for parameters of interest. Fifth and perhaps most importantly, when a random sample from the posterior distribution (such as MCMC output) is available, …
A Posterior-Based Wald-Type Statistic For Hypothesis Testing, Yong Li, Xiaobin Liu, Tao Zeng, Jun Yu
A Posterior-Based Wald-Type Statistic For Hypothesis Testing, Yong Li, Xiaobin Liu, Tao Zeng, Jun Yu
Research Collection School Of Economics
A new Wald-type statistic is proposed for hypothesis testing based on Bayesian posterior distributions under the correct model specification. The new statistic can be explained as a posterior version of the Wald statistic and has several nice properties. First, it is well-defined under improper prior distributions. Second, it avoids Jeffreys–Lindley–Bartlett’s paradox. Third, under the null hypothesis and repeated sampling, it follows a χ2" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">χ2 …