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Nonparametric density estimation from data with a mixture of Berkson and classical errors
Author(s) -
Delaigle Aurore
Publication year - 2007
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.5550350109
Subject(s) - estimator , unobservable , nonparametric statistics , observational error , density estimation , convergence (economics) , variable (mathematics) , statistics , rate of convergence , mathematics , sample (material) , sample size determination , algorithm , computer science , econometrics , key (lock) , mathematical analysis , chemistry , computer security , chromatography , economics , economic growth
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.