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Bootstrap Methods for Median Regression Models

Author

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  • Joel L. Horowitz

Abstract

The least-absolute-deviations (LAD) estimator for a median-regression or censored median-regression model does not satisfy the standard conditions for obtaining asymptotic refinements through use of the bootstrap because the LAD objective function is not smooth. This paper overcomes this problem by smoothing the objective function. The smoothed estimator is asymptotically equivalent to the ordinary LAD estimator. With bootstrap critical values, the rejection probabilities of symmetrical t and chi-square tests based on the smoothed estimator are correct to nearly order 1/n under the null hypothesis. In contrast, first-order asymptotic approximations make errors of this size.

Suggested Citation

  • Joel L. Horowitz, 1998. "Bootstrap Methods for Median Regression Models," Econometrica, Econometric Society, vol. 66(6), pages 1327-1352, November.
    • Handle: RePEc:ecm:emetrp:v:66:y:1998:i:6:p:1327-1352
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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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