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Consistency of M-Estimates in General Regression Models

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  • Liese, F.
  • Vajda, I.

Abstract

This paper extends the results of Chen and Wu [1] concerning consistency of M-estimators in the linear regression model. We consider M-estimators defined by [formula] in the general regression model yi = f(xi,[theta] ) + [epsilon]i, where f(x, [theta]) is continuous on a separable metric space X [circle times operator] [Theta], (x1, x2, ... ) is a deterministic design of experiment, and ([epsilon]1, [epsilon]2, ... ) are independet errors. This model has been considered previously by Richardson and Bhattacharyya [9], but they were restricted to [rho](x) = and their method differs from ours.

Suggested Citation

  • Liese, F. & Vajda, I., 1994. "Consistency of M-Estimates in General Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 93-114, July.
    • Handle: RePEc:eee:jmvana:v:50:y:1994:i:1:p:93-114
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    Cited by:

    1. 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.
    2. Bantli, Faouzi El & Hallin, Marc, 1999. "L1-estimation in linear models with heterogeneous white noise," Statistics & Probability Letters, Elsevier, vol. 45(4), pages 305-315, December.
    3. Søren Johansen & Lukasz Gatarek, 2014. "Optimal hedging with the cointegrated vector autoregressive model," CREATES Research Papers 2014-40, Department of Economics and Business Economics, Aarhus University.
    4. Vajda, Igor & Janzura, Martin, 1997. "On asymptotically optimal estimates for general observations," Stochastic Processes and their Applications, Elsevier, vol. 72(1), pages 27-45, December.
    5. 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.
    6. Yannis Yatracos, 2006. "On Consistent Statistical Procedures in Regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 379-387, June.
    7. Friedrich Liese & Igor Vajda, 1995. "Necessary and sufficient conditions for consistency of generalizedM-estimates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 42(1), pages 291-324, December.
    8. Liebscher, Eckhard, 2003. "Strong convergence of estimators in nonlinear autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 247-261, February.

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