
arXiv: 1401.3362
AbstractGiven a sample from we construct kernel density estimators for , the convolution of with a known error density . This problem is known as density estimation with Berkson error and has applications in epidemiology and astronomy. Little is understood about bandwidth selection for Berkson density estimation. We compare three approaches to selecting the bandwidth both asymptotically, using large‐sample approximations to the , and at finite samples, using simulations. Our results highlight the relationship between the structure of the error and the optimal bandwidth. In particular the results demonstrate the importance of smoothing when the error term is concentrated near 0. We propose a data‐driven bandwidth estimator and test its performance on NO exposure data. The Canadian Journal of Statistics 44: 142–160; 2016 © 2016 Statistical Society of Canada
FOS: Computer and information sciences, Berkson error, multivariate density estimation, Methodology (stat.ME), Density estimation, Asymptotic properties of nonparametric inference, kernel density estimation, Applications of statistics to environmental and related topics, Characterization and structure theory for multivariate probability distributions; copulas, bandwidth selection, measurement error, Statistics - Methodology
FOS: Computer and information sciences, Berkson error, multivariate density estimation, Methodology (stat.ME), Density estimation, Asymptotic properties of nonparametric inference, kernel density estimation, Applications of statistics to environmental and related topics, Characterization and structure theory for multivariate probability distributions; copulas, bandwidth selection, measurement error, Statistics - Methodology
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