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Strong consistency of M-estimates in linear models

Author

Listed:
  • Chen, X. R.
  • Wu, Y. H.

Abstract

This article studies the strong consistency of M-estimates in linear regression models directly from the minimization problem 75, where X1. X2, ... can be random observations of a p-dimensional random vector X, or that they are simply known nonrandom p-vectors. It is shown that the solution ([alpha]n, [beta]'n) of this minimization problem converges with probability one to the true parameter ([alpha]0,[beta]'0) under very general conditions on the function [varrho] and the sequence {(X'i, Yi)}.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:27:y:1988:i:1:p:116-130
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    Citations

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    Cited by:

    1. 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.
    2. Søren Johansen & Bent Nielsen, 2016. "Tightness of M-estimators for multiple linear regression in time for multiple linear regression in time series," Discussion Papers 16-05, University of Copenhagen. Department of Economics.
    3. Søren Johansen & Bent Nielsen, 2016. "Tightness of M-estimators for multiple linear regression in time series," CREATES Research Papers 2016-18, Department of Economics and Business Economics, Aarhus University.
    4. Søren Johansen & Bent Nielsen, 2014. "Outlier detection algorithms for least squares time series regression," Economics Papers 2014-W04, Economics Group, Nuffield College, University of Oxford.
    5. Xin Deng & Xuejun Wang, 2018. "Asymptotic Property of M Estimator in Classical Linear Models Under Dependent Random Errors," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1069-1090, December.
    6. Lukasz Gatarek & Søren Johansen, 2014. "Optimal hedging with the cointegrated vector autoregressive model," Discussion Papers 14-22, University of Copenhagen. Department of Economics.
    7. Søren Johansen & Bent Nielsen, 2016. "Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 321-348, June.
    8. Xin Deng & Xuejun Wang, 2020. "An exponential inequality and its application to M estimators in multiple linear models," Statistical Papers, Springer, vol. 61(4), pages 1607-1627, August.

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