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A Convolution Estimator for the Density of Nonlinear Regression Observations

Author

Listed:
  • Støve, Bård

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

  • Tjøstheim, Dag

    (Dept. of Mathematics, University of Bergen)

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.

Suggested Citation

  • Støve, Bård & Tjøstheim, Dag, 2007. "A Convolution Estimator for the Density of Nonlinear Regression Observations," Discussion Papers 2007/25, Norwegian School of Economics, Department of Business and Management Science.
    • Handle: RePEc:hhs:nhhfms:2007_025
    as

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    File URL: http://hdl.handle.net/11250/163902
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    References listed on IDEAS

    as
    1. Sam Efromovich & Alexander Samarov, 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, June.
    2. Saavedra, Ángeles & Cao, Ricardo, 1999. "Rate of convergence of a convolution-type estimator of the marginal density of a MA(1) process," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 129-155, April.
    3. Hall, Peter & Marron, J. S., 1987. "Estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 109-115, November.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Convergence rate; Convolution estimator; Kernel function; Mean squared error; Nonparametric density estimation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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