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On necessary conditions for the weak consistency of minimum L1-norm estimates in linear models

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  • Bai, Z. D.
  • Wu, Y.

Abstract

Consider the model yi = x'i[beta]0 + ei, I = 1,...,n. Under very weak conditions on the error distributions, it is shown that is a necessary conditions for the weak consistency of a minimum L1-norm estimate of [beta]0, which cannot be further improved.

Suggested Citation

  • Bai, Z. D. & Wu, Y., 1997. "On necessary conditions for the weak consistency of minimum L1-norm estimates in linear models," Statistics & Probability Letters, Elsevier, vol. 34(2), pages 193-199, June.
    • Handle: RePEc:eee:stapro:v:34:y:1997:i:2:p:193-199
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    References listed on IDEAS

    as
    1. Chen, X. R. & Wu, Y. H., 1988. "Strong consistency of M-estimates in linear models," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 116-130, October.
    2. Wu, Yuehua, 1988. "Strong consistency and exponential rate of the "minimum L1-norm" estimates in linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 6(3), pages 285-295, April.
    3. Amemiya, Takeshi, 1982. "Two Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 50(3), pages 689-711, May.
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    More about this item

    Keywords

    Minimum L1 norm estimate Weak consistency Linear regression model Necessary condition;

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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