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Combining kernel estimators in the uniform deconvolution problem
Author(s) -
van Es Bert
Publication year - 2011
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2011.00485.x
Subject(s) - mathematics , pointwise , estimator , extremum estimator , multivariate kernel density estimation , invariant estimator , minimum variance unbiased estimator , asymptotic distribution , kernel density estimation , trimmed estimator , deconvolution , m estimator , mean squared error , efficient estimator , statistics , kernel method , variable kernel density estimation , mathematical analysis , computer science , artificial intelligence , support vector machine
We construct a density estimator and an estimator of the distribution function in the uniform deconvolution model. The estimators are based on inversion formulas and kernel estimators of the density of the observations and its derivative. Initially the inversions yield two different estimators of the density and two estimators of the distribution function. We construct asymptotically optimal convex combinations of these two estimators. We also derive pointwise asymptotic normality of the resulting estimators, the pointwise asymptotic biases and an expansion of the mean integrated squared error of the density estimator. It turns out that the pointwise limit distribution of the density estimator is the same as the pointwise limit distribution of the density estimator introduced by Groeneboom and Jongbloed ( Neerlandica , 57, 2003, 136), a kernel smoothed nonparametric maximum likelihood estimator of the distribution function.