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Robust Estimation of Multiple Regression Model with Non-normal Error: Symmetric Distribution

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Author Info
Wing-Keung Wong
Guorui Bian

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Abstract

In this paper, we develop the modified maximum likelihood (MML) estimators for the multiple regression coefficients in linear model with the underlying distribution assumed to be symmetric, one of Student's t family. We obtain the closed form of the estimators and derive their asymptotic properties. In addition, we demonstrate that the MML estimators are more appropriate to estimate the parameters in the Capital Asset Pricing Model by comparing its performance with that of least squares estimators (LSE) on the monthly returns of US portfolios. Our empirical study reveals that the MML estimators are more efficient than the LSE in terms of relative efficiency of one-step-ahead forecast mean square error for small samples.

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File URL: http://www.buseco.monash.edu.au/eco/research/papers/2005/0905mregressionmodel.pdf
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Publisher Info
Paper provided by Monash University, Department of Economics in its series Monash Economics Working Papers with number 09/05.

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Length: 18 pages
Date of creation: 01 Jun 2005
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Handle: RePEc:mos:moswps:2005-09

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Related research
Keywords: Maximum likelihood estimators; Modified maximum likelihood estimators; Student's t family; Capital Asset Pricing Model; Robustness.;

Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
G1 - Financial Economics - - General Financial Markets

This paper has been announced in the following NEP Reports:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January. [Downloadable!] (restricted)
  2. Wong, Wing-Keung & Bian, Guorui, 2005. "Estimating parameters in autoregressive models with asymmetric innovations," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 61-70, January. [Downloadable!] (restricted)
    Other versions:
  3. Wing-Keung Wong & Raymond H. Chan, 2004. "On the Estimation of Cost of Capital and its Reliability," Departmental Working Papers wp0401, National University of Singapore, Department of Economics. [Downloadable!]
  4. Clements, Michael P. & Hendry, David F., 1997. "An empirical study of seasonal unit roots in forecasting," International Journal of Forecasting, Elsevier, vol. 13(3), pages 341-355, September. [Downloadable!] (restricted)
  5. Hsiao, Cheng, 1989. "Consistent estimation for some nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 41(1), pages 159-185, May. [Downloadable!] (restricted)
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  6. Amemiya, Yasuo, 1985. "Instrumental variable estimator for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 28(3), pages 273-289, June. [Downloadable!] (restricted)
  7. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," Journal of Business, University of Chicago Press, vol. 36, pages 420. [Downloadable!]
  8. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September. [Downloadable!] (restricted)
  9. Honore, Bo E. & Hu, Luojia, 2004. "Estimation of cross sectional and panel data censored regression models with endogeneity," Journal of Econometrics, Elsevier, vol. 122(2), pages 293-316, October. [Downloadable!] (restricted)
  10. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-52, September. [Downloadable!] (restricted)
  11. Harvey, Campbell R. & Zhou, Guofu, 1993. "International asset pricing with alternative distributional specifications," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 107-131, June. [Downloadable!] (restricted)
  12. Hausman, J. A. & Abrevaya, Jason & Scott-Morton, F. M., 1998. "Misclassification of the dependent variable in a discrete-response setting," Journal of Econometrics, Elsevier, vol. 87(2), pages 239-269, September. [Downloadable!] (restricted)
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