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Department of Business and Management Science, Norwegian School of Economics (NHH) Discussion Papers, Department of Business and Management Science, Norwegian School of Economics (NHH)

No 2007/25:
A Convolution Estimator for the Density of Nonlinear Regression Observations

Bård Støve () and Dag Tjøstheim ()

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.

Keywords: Convergence rate; Convolution estimator; Kernel function; Mean squared error; Nonparametric density estimation; (follow links to similar papers)

JEL-Codes: C13; (follow links to similar papers)

33 pages, November 30, 2007

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