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Higher Order Bias Correcting Moment Equation for M-Estimation and Its Higher Order Efficiency

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  • Kyoo Il Kim

    (Department of Economics, Michigan State University, 486W Circle Dr, East Lansing, MI 48824, USA)

Abstract

This paper studies an alternative bias correction for the M-estimator, which is obtained by correcting the moment equations in the spirit of Firth (1993). In particular, this paper compares the stochastic expansions of the analytically-bias-corrected estimator and the alternative estimator and finds that the third-order stochastic expansions of these two estimators are identical. This implies that at least in terms of the third-order stochastic expansion, we cannot improve on the simple one-step bias correction by using the bias correction of moment equations. This finding suggests that the comparison between the one-step bias correction and the method of correcting the moment equations or the fully-iterated bias correction should be based on the stochastic expansions higher than the third order.

Suggested Citation

  • Kyoo Il Kim, 2016. "Higher Order Bias Correcting Moment Equation for M-Estimation and Its Higher Order Efficiency," Econometrics, MDPI, vol. 4(4), pages 1-19, December.
    • Handle: RePEc:gam:jecnmx:v:4:y:2016:i:4:p:48-:d:84668
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    References listed on IDEAS

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