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A Bayesian Chi-Squared Test for Hypothesis Testing

Author

Listed:
  • Yong Li

    (Renmin University of China)

  • Xiao-Bin Liu

    (Singapore Management University)

  • Jun Yu

    (Singapore Management University, School of Economics)

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 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 appeal in practical applications. First, it is well-defined under improper prior distributions. Second, it avoids Jeffrey-Lindley’s paradox. Third, it is relatively easy to compute, even for models with latent variables. Finally, it is pivotal and its threshold value can be easily obtained from the asymptotic chi-squared distribution. The method is illustrated using some real examples in economics and finance.

Suggested Citation

  • Yong Li & Xiao-Bin Liu & Jun Yu, 2014. "A Bayesian Chi-Squared Test for Hypothesis Testing," Working Papers 03-2014, Singapore Management University, School of Economics.
    • Handle: RePEc:siu:wpaper:03-2014
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    Cited by:

    1. Antonio Parisi & B. Liseo, 2018. "Objective Bayesian analysis for the multivariate skew-t model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 277-295, June.
    2. Zhang, Yonghui & Chen, Zhongtian & Li, Yong, 2017. "Bayesian testing for short term interest rate models," Finance Research Letters, Elsevier, vol. 20(C), pages 146-152.
    3. Cross, Jamie L. & Hou, Chenghan & Trinh, Kelly, 2021. "Returns, volatility and the cryptocurrency bubble of 2017–18," Economic Modelling, Elsevier, vol. 104(C).
    4. Li, Yong & Yu, Jun & Zeng, Tao, 2018. "Specification tests based on MCMC output," Journal of Econometrics, Elsevier, vol. 207(1), pages 237-260.
    5. Liu, Xiaobin & Li, Yong & Yu, Jun & Zeng, Tao, 2022. "Posterior-based Wald-type statistics for hypothesis testing," Journal of Econometrics, Elsevier, vol. 230(1), pages 83-113.
    6. Chen, Shyh-Wei & Hsu, Chi-Sheng & Xie, Zixong, 2016. "Are there periodically collapsing bubbles in the stock markets? New international evidence," Economic Modelling, Elsevier, vol. 52(PB), pages 442-451.
    7. Yong Li & Xiaobin Liu & Jun Yu & Tao Zeng, 2018. "A New Wald Test for Hypothesis Testing Based on MCMC outputs," Papers 1801.00973, arXiv.org.
    8. Doğan, Osman & Taşpınar, Süleyman & Bera, Anil K., 2021. "A Bayesian robust chi-squared test for testing simple hypotheses," Journal of Econometrics, Elsevier, vol. 222(2), pages 933-958.
    9. Jin-Yu Zhang & Zhong-Tian Chen & Yong Li, 2019. "Bayesian Testing for Leverage Effect in Stochastic Volatility Models," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1153-1164, March.
    10. Yong Li & Jun Yu, 2019. "An Improved Bayesian Unit Root Test in Stochastic Volatility Models," Annals of Economics and Finance, Society for AEF, vol. 20(1), pages 103-122, May.
    11. Guanhao Feng & Jingyu He, 2019. "Factor Investing: A Bayesian Hierarchical Approach," Papers 1902.01015, arXiv.org, revised Sep 2020.

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    More about this item

    Keywords

    Bayes factor; Decision theory; EM algorithm; Lagrange multiplier; Markov chain Monte Carlo; Latent variable models;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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