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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.

Suggested Citation

  • Wing-Keung Wong & Guorui Bian, 2005. "Robust Estimation of Multiple Regression Model with Non-normal Error: Symmetric Distribution," Monash Economics Working Papers 09/05, Monash University, Department of Economics.
  • Handle: RePEc:mos:moswps:2005-09
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    File URL: http://www.buseco.monash.edu.au/eco/research/papers/2005/0905mregressionmodel.pdf
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    References listed on IDEAS

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    More about this item

    Keywords

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

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • G1 - Financial Economics - - General Financial Markets

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