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Bahadur Representation for the Nonparametric M-Estimator Under Alpha-mixing Dependence

Author

Listed:
  • Yebin Cheng

    (Faculty of Economics and Econometrics, Universiteit van Amsterdam)

  • Jan G. de Gooijer

    (Faculty of Economics and Econometrics, Universiteit van Amsterdam)

Abstract

Under the condition that the observations, which come from a high-dimensional population (X,Y), are strongly stationary and strongly-mixing, through using the local linear method, we investigate, in this paper, the strong Bahadur representation of the nonparametric M-estimator for the unknown function m(x)=arg minaIE(r(a,Y)|X=x), where the loss function r(a,y) is measurable. Furthermore, some related simulations are illustrated by using the cross validation method for both bivariate linear and bivariate nonlinear time series contaminated by heavy-tailed errors. The M-estimator is applied to a series of S&P 500 index futures andspot prices to compare its performance in practice with the "usual" squared-loss regression estimator.

Suggested Citation

  • Yebin Cheng & Jan G. de Gooijer, 2005. "Bahadur Representation for the Nonparametric M-Estimator Under Alpha-mixing Dependence," Tinbergen Institute Discussion Papers 05-067/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20050067
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    References listed on IDEAS

    as
    1. Toshio Honda, 2000. "Nonparametric Estimation of a Conditional Quantile for α-Mixing Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 459-470, September.
    2. Masry, Elias, 1996. "Multivariate regression estimation local polynomial fitting for time series," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 81-101, December.
    3. Liebscher E., 2001. "Estimation Of The Density And The Regression Function Under Mixing Conditions," Statistics & Risk Modeling, De Gruyter, vol. 19(1), pages 9-26, January.
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    More about this item

    Keywords

    Asymptotic representation; Kernel function; Robust estimator; Strongly-mixing;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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