A posterior-based Wald-type statistic for hypothesis testing

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 prio...

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Main Authors: LI, Yong, LIU, Xiaobin, ZENG, Tao, YU, Jun
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Language:English
Published: Institutional Knowledge at Singapore Management University 2022
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Online Access:https://ink.library.smu.edu.sg/soe_research/2172
https://ink.library.smu.edu.sg/context/soe_research/article/3172/viewcontent/ABT33_.pdf
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spelling sg-smu-ink.soe_research-31722022-11-30T08:04:34Z A posterior-based Wald-type statistic for hypothesis testing LI, Yong LIU, Xiaobin ZENG, Tao YU, Jun 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 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, 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 random samples. A robust version of the test statistic is developed under model misspecification and inherits many nice properties of the new posterior statistic. The finite sample performance of the statistics is examined in Monte Carlo studies. The method is applied to two latent variable models used in microeconometrics and financial econometrics. 2022-03-01T08:00:00Z text application/pdf https://ink.library.smu.edu.sg/soe_research/2172 info:doi/10.1016/j.jeconom.2021.11.003 https://ink.library.smu.edu.sg/context/soe_research/article/3172/viewcontent/ABT33_.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Economics eng Institutional Knowledge at Singapore Management University Decision theory Hypothesis testing Latent variable models Posterior simulation Wald test. Econometrics
institution Singapore Management University
building SMU Libraries
continent Asia
country Singapore
Singapore
content_provider SMU Libraries
collection InK@SMU
language English
topic Decision theory
Hypothesis testing
Latent variable models
Posterior simulation
Wald test.
Econometrics
spellingShingle Decision theory
Hypothesis testing
Latent variable models
Posterior simulation
Wald test.
Econometrics
LI, Yong
LIU, Xiaobin
ZENG, Tao
YU, Jun
A posterior-based Wald-type statistic for hypothesis testing
description 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 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, 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 random samples. A robust version of the test statistic is developed under model misspecification and inherits many nice properties of the new posterior statistic. The finite sample performance of the statistics is examined in Monte Carlo studies. The method is applied to two latent variable models used in microeconometrics and financial econometrics.
format text
author LI, Yong
LIU, Xiaobin
ZENG, Tao
YU, Jun
author_facet LI, Yong
LIU, Xiaobin
ZENG, Tao
YU, Jun
author_sort LI, Yong
title A posterior-based Wald-type statistic for hypothesis testing
title_short A posterior-based Wald-type statistic for hypothesis testing
title_full A posterior-based Wald-type statistic for hypothesis testing
title_fullStr A posterior-based Wald-type statistic for hypothesis testing
title_full_unstemmed A posterior-based Wald-type statistic for hypothesis testing
title_sort posterior-based wald-type statistic for hypothesis testing
publisher Institutional Knowledge at Singapore Management University
publishDate 2022
url https://ink.library.smu.edu.sg/soe_research/2172
https://ink.library.smu.edu.sg/context/soe_research/article/3172/viewcontent/ABT33_.pdf
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