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A Convolution Estimator for the Density of Nonlinear Regression Observations

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  • Støve, Bård

    ()
    (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

  • Tjøstheim, Dag

    ()
    (Dept. of Mathematics, University of Bergen)

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    Abstract

    The problem of estimating an unknown density function has been widely studied. In this paper we present a convolution estimator for the density of the responses in a nonlinear regression model. The rate of convergence for the variance of the convolution estimator is of order 1/n. This is faster than the rate for the kernel density method. The intuition behind this result is that the convolution estimator uses model information, and thus an improvement can be expected. We also derive the bias of the new estimator and conduct simulation experiments to check the finite sample properties. The proposed estimator performs substantially better than the kernel density estimator for well-behaved noise densities.

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    Bibliographic Info

    Paper provided by Department of Business and Management Science, Norwegian School of Economics in its series Discussion Papers with number 2007/25.

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    Length: 33 pages
    Date of creation: 30 Nov 2007
    Date of revision:
    Handle: RePEc:hhs:nhhfms:2007_025

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    Postal: NHH, Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway
    Phone: +47 55 95 92 93
    Fax: +47 55 95 96 50
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    Web page: http://www.nhh.no/en/research-faculty/department-of-business-and-management-science.aspx
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    Related research

    Keywords: Convergence rate; Convolution estimator; Kernel function; Mean squared error; Nonparametric density estimation;

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    1. Sam Efromovich, 2000. "Adaptive Estimation of the Integral of Squared Regression Derivatives," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 27(2), pages 335-351.
    2. Hall, Peter & Marron, J. S., 1987. "Estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 109-115, November.
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