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A Shortcut to LAD Estimator Asymptotics

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Abstract

Using generalized functions of random variables and generalized Taylor series expansions, we provide almost trivial demonstrations of the asymptotic theory for the LAD estimator in a regression model setting. The approach is justified by the smoothing that is delivered in the limit by the asymptotics, whereby the generalized functions are forced to appear as linear functionals wherein they become real valued. Models with fixed and random regressors, autoregressions and autoregressions with infinite variance errors are studied. Some new analytic results are obtained including an asymptotic expansion of the distribution of the LAD estimator and the results of some earlier simulation studies are examined.

Suggested Citation

  • Peter C.B. Phillips, 1990. "A Shortcut to LAD Estimator Asymptotics," Cowles Foundation Discussion Papers 949, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:949
    Note: CFP 801.
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