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Root n consistent density estimators for sums of independent random variables
Authors:
Anton Schick a;
Wolfgang wefelmeyer b
| Affiliations: | a Department of Mathematical Sciences, Binghamton University, Binghamton, NY, USA |
b Mathematisches Institut, Universit t zu K ln, Kln, Germany |
DOI:
10.1080/10485250410001713990
Publication Frequency:
8 issues per year
Published in:
Journal of Nonparametric Statistics,
Volume
16,
Issue
6
December
2004
, pages 925
- 935
Journal of Nonparametric Statistics,
Volume
16,
Issue
6
December
2004
, pages 925
- 935
Subjects:
Mathematical Economics;
Mathematical Finance;
Medical Statistics;
Statistical Theory & Methods;
Statistics;
Statistics for the Biological Sciences;
Stochastic Models & Processes;
Number of References: 21
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Abstract
The density of a sum of independent random variables can be estimated by the convolution of kernel estimators for the marginal densities. We show under mild conditions that the resulting estimator is n1/2-consistent and converges in distribution in the spaces C0(
 ) and L1 to a centered Gaussian process.
|
| Keywords: Plug-in estimator; Kernel density estimator; Parametric convergence rate; von Mises statistic; Functional central limit theorem |
| view references (21) |
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