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A Convolution Estimator for the Density of Nonlinear Regression Observations
Author(s) -
STØVE BÅRD,
TJØSTHEIM DAG
Publication year - 2012
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2011.00762.x
Subject(s) - mathematics , estimator , mean squared error , kernel density estimation , convolution (computer science) , statistics , kernel (algebra) , minimum variance unbiased estimator , consistent estimator , rate of convergence , bias of an estimator , efficient estimator , discrete mathematics , computer science , computer network , channel (broadcasting) , artificial neural network , machine learning
. The problem of estimating an unknown density function has been widely studied. In this article, we present a convolution estimator for the density of the responses in a nonlinear heterogenous regression model. The rate of convergence for the mean square error of the convolution estimator is of order n −1 under certain regularity conditions. This is faster than the rate for the kernel density method. We derive explicit expressions for the asymptotic variance and the bias of the new estimator, and further a data‐driven bandwidth selector is proposed. We conduct simulation experiments to check the finite sample properties, and the convolution estimator performs substantially better than the kernel density estimator for well‐behaved noise densities.