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

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  • Wing-Keung Wong
  • Guorui Bian

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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Bibliographic 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
Date of revision:
Handle: RePEc:mos:moswps:2005-09

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

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  1. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July.
  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.
  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.
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  12. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420.
  13. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
  14. 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.
  15. 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.
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