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Robust and Partially Adaptive Estimation of Regression Models

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  • Butler, Richard J, et al
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    Abstract

    It is well known that least squares estimates can be very sensitive to departures from normality. Various robust estimators, such as least absolute deviations, L(superscript "p") estimators or M-estimators provide possible alternatives to least squares when such departures occur. This paper applies a partially adaptive technique to estimate the parameters of William F. Sharpe's market model. This methodology is based on a generalized t-distribution and includes as special cases least squares, least absolute deviation, and L(superscript "p"), as well as some estimation procedures that have bounded and redescending influence functions. Coauthors are James B.McDonald, Ray D. Nelson, and Steven B. White. Copyright 1990 by MIT Press.

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    Bibliographic Info

    Article provided by MIT Press in its journal Review of Economics & Statistics.

    Volume (Year): 72 (1990)
    Issue (Month): 2 (May)
    Pages: 321-27

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    Handle: RePEc:tpr:restat:v:72:y:1990:i:2:p:321-27

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    Cited by:
    1. James B. McDonald & Hieu Nguyen, 2012. "Heteroskedasticity and Distributional Assumptions in the Censored Regression Model," BYU Macroeconomics and Computational Laboratory Working Paper Series 2012-09, Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory.
    2. Fong, Wai Mun, 1997. "Robust beta estimation: Some empirical evidence," Review of Financial Economics, Elsevier, vol. 6(2), pages 167-186.
    3. Bönte, G., 1995. "Evaluierung adaptiver Hochrechnungsverfahren," Discussion Papers 05/1995, Friedrich-Alexander-University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    4. Usta, Ilhan & Kantar, Yeliz Mert, 2011. "On the performance of the flexible maximum entropy distributions within partially adaptive estimation," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2172-2182, June.
    5. Steven Caudill, 2012. "A partially adaptive estimator for the censored regression model based on a mixture of normal distributions," Statistical Methods and Applications, Springer, vol. 21(2), pages 121-137, June.
    6. Arslan, Olcay, 2009. "Maximum likelihood parameter estimation for the multivariate skew-slash distribution," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2158-2165, October.
    7. Stefan Mittnik & Marc Paolella & Svetlozar Rachev, 1998. "Unconditional and Conditional Distributional Models for the Nikkei Index," Asia-Pacific Financial Markets, Springer, vol. 5(2), pages 99-128, May.
    8. Mikosch, Thomas & de Vries, Casper G., 2013. "Heavy tails of OLS," Journal of Econometrics, Elsevier, vol. 172(2), pages 205-221.
    9. Steven Caudill & James Long, 2010. "Do former athletes make better managers? Evidence from a partially adaptive grouped-data regression model," Empirical Economics, Springer, vol. 39(1), pages 275-290, August.
    10. Grottke, Martin, 1999. "Generierung schiefer Verteilungen mittels Skalenparametersplittung," Discussion Papers 30/1999, Friedrich-Alexander-University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    11. Luca Greco & Laura Ventura, 2006. "Bounded Estimation in the Presence of Nuisance Parameters," Statistical Methods and Applications, Springer, vol. 15(1), pages 27-36, May.
    12. Katherine G. Yewell & Steven B. Caudill & Franklin G. Mixon, Jr., 2014. "Referee Bias and Stoppage Time in Major League Soccer: A Partially Adaptive Approach," Econometrics, MDPI, Open Access Journal, vol. 2(1), pages 1-19, February.
    13. Olcay Arslan, 2010. "An alternative multivariate skew Laplace distribution: properties and estimation," Statistical Papers, Springer, vol. 51(4), pages 865-887, December.

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