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Tightness of M-estimators for multiple linear regression in time for multiple linear regression in time series

Author

Listed:
  • Søren Johansen

    (Department of Economics, University of Copenhagen)

  • Bent Nielsen

    (Department of Economics, Nuffield College)

Abstract

We show tightness of a general M-estimator for multiple linear regression in time series. The positive criterion function for the M-estimator is assumed lower semi-continuous and sufficiently large for large argument: Particular cases are the Huber-skip and quantile regression. Tightness requires an assumption on the frequency of small regressors. We show that this is satis?ed for a variety of deterministic and stochastic regressors, including stationary an random walks regressors. The results are obtained using a detailed analysis of the condition on the regressors combined with some recent martingale results.

Suggested Citation

  • 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.
    • Handle: RePEc:kud:kuiedp:1605
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    File URL: http://www.econ.ku.dk/english/research/publications/wp/dp_2016/1605.pdf
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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.
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    More about this item

    Keywords

    M-estimator; robust statistics; martingales; Huber-skip; quantile estimation.;
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