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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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Related research

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

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  1. Hsiao, Cheng, 1989. "Consistent estimation for some nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 41(1), pages 159-185, May.
  2. Wing-Keung Wong & Guorui Bian, 2004. "Estimating Parameters in Autoregressive Models with Asymmetric Innovations," Departmental Working Papers wp0408, National University of Singapore, Department of Economics.
  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.
  4. Drost, F.C. & Nijman, T.E., 1992. "Temporal Aggregation of Garch Processes," Papers 9240, Tilburg - Center for Economic Research.
  5. 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.
  6. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
  7. 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.
  8. Sharpe, William F., 1967. "Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(02), pages 76-84, June.
  9. Li, Tong & Hsiao, Cheng, 2004. "Robust estimation of generalized linear models with measurement errors," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 51-65.
  10. 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.
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  12. 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.
  13. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420.
  14. 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.
  15. Amemiya, Yasuo, 1985. "Instrumental variable estimator for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 28(3), pages 273-289, June.
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