Title

A Bayesian chi-squared test for hypothesis testing

Publication Type

Journal Article

Publication Date

11-2015

Abstract

A new Bayesian test statistic is proposed to test a point null hypothesis based on a quadratic loss. The proposed test statistic may be regarded as the Bayesian version of the Lagrange multiplier test. Its asymptotic distribution is obtained based on a set of regular conditions and follows a chi-squared distribution when the null hypothesis is correct. The new statistic has several important advantages that make it appealing in practical applications. First, it is well-defined under improper prior distributions. Second, it avoids Jeffrey-Lindley's paradox. Third, it always takes a non-negative value and is relatively easy to compute, even for models with latent variables. Fourth, its numerical standard error is relatively easy to obtain. Finally, it is asymptotically pivotal and its threshold values can be obtained from the chi-squared distribution. The method is illustrated using some real examples in economics and finance.

Keywords

Bayes factor, Decision theory, EM algorithm, Lagrange multiplier, Markov chain Monte Carlo, Latent variable models

Discipline

Econometrics

Research Areas

Econometrics

Publication

Journal of Econometrics

Volume

189

Issue

1

First Page

54

Last Page

69

ISSN

0304-4076

Identifier

10.1016/j.jeconom.2015.06.021

Publisher

Elsevier

Copyright Owner and License

Authors with CC-BY-NC-ND

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Additional URL

http://dx.doi.org/10.1016/j.jeconom.2015.06.021

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