Combining kernel estimators in the uniform deconvolution problem
Article first published online: 28 APR 2011
© 2011 The Author. Statistica Neerlandica © 2011 VVS
Volume 65, Issue 3, pages 275–296, August 2011
How to Cite
van Es, B. (2011), Combining kernel estimators in the uniform deconvolution problem. Statistica Neerlandica, 65: 275–296. doi: 10.1111/j.1467-9574.2011.00485.x
- Issue published online: 12 JUL 2011
- Article first published online: 28 APR 2011
- Received: June 2010. Revised: January 2011.
- uniform deconvolution;
- kernel estimation;
- asymptotic normality
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.