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Root "n" consistent and optimal density estimators for moving average processes

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  • Anton Schick
  • Wolfgang Wefelmeyer
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    Abstract

    The marginal density of a first order moving average process can be written as a convolution of two innovation densities. Saavedra & Cao [Can. J. Statist. (2000), 28, 799] propose to estimate the marginal density by plugging in kernel density estimators for the innovation densities, based on estimated innovations. They obtain that for an appropriate choice of bandwidth the variance of their estimator decreases at the rate 1/"n". Their estimator can be interpreted as a specific "U"-statistic. We suggest a slightly simplified "U"-statistic as estimator of the marginal density, prove that it is asymptotically normal at the same rate, and describe the asymptotic variance explicitly. We show that the estimator is asymptotically efficient if no structural assumptions are made on the innovation density. For innovation densities known to have mean zero or to be symmetric, we describe improvements of our estimator which are again asymptotically efficient. Copyright Board of the Foundation of the Scandinavian Journal of Statistics 2004.

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    Bibliographic Info

    Article provided by Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association in its journal Scandinavian Journal of Statistics.

    Volume (Year): 31 (2004)
    Issue (Month): 1 ()
    Pages: 63-78

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    Handle: RePEc:bla:scjsta:v:31:y:2004:i:1:p:63-78

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    Cited by:
    1. Dabo-Niang, Sophie & Francq, Christian & Zakoian, Jean-Michel, 2009. "Combining parametric and nonparametric approaches for more efficient time series prediction," MPRA Paper 16893, University Library of Munich, Germany.
    2. Escanciano, Juan Carlos & Jacho-Chávez, David T., 2012. "n-uniformly consistent density estimation in nonparametric regression models," Journal of Econometrics, Elsevier, vol. 167(2), pages 305-316.
    3. Anton Schick & Wolfgang Wefelmeyer, 2008. "Root-n consistency in weighted L 1 -spaces for density estimators of invertible linear processes," Statistical Inference for Stochastic Processes, Springer, vol. 11(3), pages 281-310, October.
    4. Dabo-Niang, Sophie & Francq, Christian & Zakoïan, Jean-Michel, 2010. "Combining Nonparametric and Optimal Linear Time Series Predictions," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1554-1565.
    5. Ao Yuan & Jan G. De Gooijer, 2006. "Semiparametric Regression with Kernel Error Model," Tinbergen Institute Discussion Papers 06-058/4, Tinbergen Institute.

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