Nonparametric density estimation from data with a mixture of Berkson and classical errors |
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Authors: | Aurore Delaigle |
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Institution: | Department of Mathematics, University of Bristol Bristol BS8 1TW, England, UK |
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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 simulations and on a real data example. |
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Keywords: | Bandwidth selection deconvolution density estimation errors in variables kernel method smoothing |
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