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Asymptotic uniform linearity of some robust statistics under exponentially subordinated strongly dependent models

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  • Chen, Shijie
  • Mukherjee, Kanchan

Abstract

In this paper, we discuss an asymptotic distributional theory of three broad classes of robust estimators of the regression parameter namely, L-, M- and R-estimators in a linear regression model when the errors are generated by an exponentially subordinated strongly dependent process. The results are obtained as a consequence of an asymptotic uniform Taylor-type expansion of certain randomly weighted empirical processes. The limiting distributions of the estimators are nonnormal and depend on the first nonzero index of the Laguerre polynomial expansion of a class of indicator functions of the error random variables.

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  • Chen, Shijie & Mukherjee, Kanchan, 1999. "Asymptotic uniform linearity of some robust statistics under exponentially subordinated strongly dependent models," Statistics & Probability Letters, Elsevier, vol. 44(2), pages 137-146, August.
    • Handle: RePEc:eee:stapro:v:44:y:1999:i:2:p:137-146
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    References listed on IDEAS

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    1. Roger W. Koenker & Vasco D'Orey, 1987. "Computing Regression Quantiles," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 383-393, November.
    2. Koul, H. L. & Mukherjee, K., 1994. "Regression Quantiles and Related Processes Under Long Range Dependent Errors," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 318-337, November.
    3. Roger Koenker & Vasco d'Orey, 1994. "A Remark on Algorithm as 229: Computing Dual Regression Quantiles and Regression Rank Scores," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(2), pages 410-414, June.
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    Cited by:

    1. Beran, Jan, 2006. "On location estimation for LARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1766-1782, September.

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