Scandinavian Working Papers in Business Administration

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

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

Bård Støve () and Dag Tjøstheim ()
Additional contact information
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.

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

JEL-codes: C13

33 pages, November 30, 2007

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