() and Dag Tjøstheim
Bård Støve: Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration, Postal: NHH , Department of Finance and Management Science, Helleveien 30, N-5045 Bergen, Norway
Dag Tjøstheim: Dept. of Mathematics, University of Bergen, Postal: University of Bergen, Department of Mathematics, Johannes Bruns gate 12, N-5008 Bergen, Norway
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.
33 pages, November 30, 2007
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