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  1. Annals of the Institute of Statistical Mathematics
  2. Annals of the Institute of Statistical Mathematics : Volume 64
  3. Annals of the Institute of Statistical Mathematics : Volume 64, Issue 5, October 2012
  4. On estimating distribution functions using Bernstein polynomials
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Annals of the Institute of Statistical Mathematics : Volume 69
Annals of the Institute of Statistical Mathematics : Volume 68
Annals of the Institute of Statistical Mathematics : Volume 67
Annals of the Institute of Statistical Mathematics : Volume 66
Annals of the Institute of Statistical Mathematics : Volume 65
Annals of the Institute of Statistical Mathematics : Volume 64
Annals of the Institute of Statistical Mathematics : Volume 64, Issue 6, December 2012
Annals of the Institute of Statistical Mathematics : Volume 64, Issue 5, October 2012
An optimal modification of the LIML estimation for many instruments and persistent heteroscedasticity
Asymptotically distribution free test for parameter change in a diffusion process model
On estimating distribution functions using Bernstein polynomials
Optimal and efficient designs for Gompertz regression models
A general transformation class of semiparametric cure rate frailty models
Some problems in nonparametric inference for the stress release process related to the local time
Density-ratio matching under the Bregman divergence: a unified framework of density-ratio estimation
Testing for a constant coefficient of variation in nonparametric regression by empirical processes
Asymptotic conditional distribution of exceedance counts: fragility index with different margins
Erratum to: A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations
Annals of the Institute of Statistical Mathematics : Volume 64, Issue 4, August 2012
Annals of the Institute of Statistical Mathematics : Volume 64, Issue 3, June 2012
Annals of the Institute of Statistical Mathematics : Volume 64, Issue 2, April 2012
Annals of the Institute of Statistical Mathematics : Volume 64, Issue 1, February 2012
Annals of the Institute of Statistical Mathematics : Volume 63
Annals of the Institute of Statistical Mathematics : Volume 62
Annals of the Institute of Statistical Mathematics : Volume 61
Annals of the Institute of Statistical Mathematics : Volume 60
Annals of the Institute of Statistical Mathematics : Volume 59
Annals of the Institute of Statistical Mathematics : Volume 58
Annals of the Institute of Statistical Mathematics : Volume 57
Annals of the Institute of Statistical Mathematics : Volume 56
Annals of the Institute of Statistical Mathematics : Volume 55
Annals of the Institute of Statistical Mathematics : Volume 54
Annals of the Institute of Statistical Mathematics : Volume 53
Annals of the Institute of Statistical Mathematics : Volume 52
Annals of the Institute of Statistical Mathematics : Volume 51
Annals of the Institute of Statistical Mathematics : Volume 50
Annals of the Institute of Statistical Mathematics : Volume 49

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On estimating distribution functions using Bernstein polynomials

Content Provider SpringerLink
Author Leblanc, Alexandre
Copyright Year 2011
Abstract It is a known fact that some estimators of smooth distribution functions can outperform the empirical distribution function in terms of asymptotic (integrated) mean-squared error. In this paper, we show that this is also true of Bernstein polynomial estimators of distribution functions associated with densities that are supported on a closed interval. Specifically, we introduce a higher order expansion for the asymptotic (integrated) mean-squared error of Bernstein estimators of distribution functions and examine the relative deficiency of the empirical distribution function with respect to these estimators. Finally, we also establish the (pointwise) asymptotic normality of these estimators and show that they have highly advantageous boundary properties, including the absence of boundary bias.
Starting Page 919
Ending Page 943
Page Count 25
File Format PDF
ISSN 00203157
Journal Annals of the Institute of Statistical Mathematics
Volume Number 64
Issue Number 5
e-ISSN 15729052
Language English
Publisher Springer Japan
Publisher Date 2011-11-20
Publisher Place Japan
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Bernstein polynomials Distribution function estimation Mean integrated squared error Mean squared error Asymptotic properties Efficiency Deficiency Statistics for Business/Economics/Mathematical Finance/Insurance Statistics
Content Type Text
Resource Type Article
Subject Statistics and Probability
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