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Dirichlet Prior for Estimating Unknown Regression Error Heteroscedasticity

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  • Hiroaki Chigira
  • Tsunemasa Shiba

Abstract

We propose a Bayesian procedure to estimate heteroscedastic variances of the regression error term ω, when the form of heteroscedasticity is unknown. The prior information on ω is based on a Dirichlet distribution, and in the Markov Chain Monte Carlo sampling, its proposal density parameters' information is elicited from the well-known Eicker-White Heteroscedasticity Consistent Variance-Covariance Matrix Estimator. We present a numerical example to show that our scheme works.

Suggested Citation

  • Hiroaki Chigira & Tsunemasa Shiba, 2012. "Dirichlet Prior for Estimating Unknown Regression Error Heteroscedasticity," Global COE Hi-Stat Discussion Paper Series gd12-248, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hst:ghsdps:gd12-248
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    References listed on IDEAS

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    1. Hiroaki Chigira & Tsunemasa Shiba, 2007. "Bayesian Estimation of Unknown Regression Error Heteroscedasticity," Hi-Stat Discussion Paper Series d07-221, Institute of Economic Research, Hitotsubashi University.
    2. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-891, July.
    3. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    4. Banz, Rolf W., 1981. "The relationship between return and market value of common stocks," Journal of Financial Economics, Elsevier, vol. 9(1), pages 3-18, March.
    5. Godfrey, L.G., 2006. "Tests for regression models with heteroskedasticity of unknown form," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2715-2733, June.
    6. Greenberg,Edward, 2014. "Introduction to Bayesian Econometrics," Cambridge Books, Cambridge University Press, number 9781107436770, January.
    7. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    8. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 19-40, Suppl. De.
    9. Chan, K C & Chen, Nai-Fu, 1991. "Structural and Return Characteristics of Small and Large Firms," Journal of Finance, American Finance Association, vol. 46(4), pages 1467-1484, September.
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    1. Doppelhofer, Gernot & Hansen, Ole-Petter Moe & Weeks, Melvyn, 2016. "Determinants of long-term economic Growth redux: A Measurement Error Model Averaging (MEMA) approach," Discussion Paper Series in Economics 19/2016, Norwegian School of Economics, Department of Economics.
    2. Ruochen Wu & Melvyn Weeks, 2020. "A Semi-Parametric Bayesian Generalized Least Squares Estimator," Papers 2011.10252, arXiv.org, revised Jan 2023.
    3. Wu, R. & Weeks, M., 2020. "A Semi-Parametric Bayesian Generalized Least Square Estimator," Cambridge Working Papers in Economics 2011, Faculty of Economics, University of Cambridge.
    4. Doppelhofer, G. & Moe Hansen, O-P. & Weeks, M., 2017. "Determinants of long-term economic growth redux: A Measurement Error Model Averaging (MEMA) approach," Cambridge Working Papers in Economics 1702, Faculty of Economics, University of Cambridge.

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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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