Journal article

Nonparametric density estimation from data with a mixture of Berkson and classical errors

Aurore Delaigle

CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE | WILEY-BLACKWELL | Published : 2007

Abstract

The author considers density estimation from contaminated data where the measurement errors come from two very different sources. A first error, of Berkson type, is incurred before the experiment: the variable X of interest is unobservable and only a surrogate can be measured. A second error, of classical type, is incurred after the experiment: the surrogate can only be observed with measurement error. The author develops two nonparametric estimators of the density of X, valid whenever Berkson, classical or a mixture of both errors are present. Rates of convergence of the estimators are derived and a fully data-driven procedure is proposed. Finite sample performance is investigated via simul..

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