On improving convergence rate of Bernstein polynomial density estimator

Gaku Igarashi and Yoshihide Kakizawa

Journal of Nonparametric Statistics, 2014, vol. 26, issue 1, 61-84

Abstract: This paper is concerned with the Bernstein estimator [Vitale, R.A. (1975), 'A Bernstein Polynomial Approach to Density Function Estimation', in Statistical Inference and Related Topics , ed. M.L. Puri, 2, New York: Academic Press, pp. 87-99] to estimate a density with support [0, 1]. One of the major contributions of this paper is an application of a multiplicative bias correction [Terrell, G.R., and Scott, D.W. (1980), 'On Improving Convergence Rates for Nonnegative Kernel Density Estimators', The Annals of Statistics , 8, 1160-1163], which was originally developed for the standard kernel estimator. Moreover, the renormalised multiplicative bias corrected Bernstein estimator is studied rigorously. The mean squared error (MSE) in the interior and mean integrated squared error of the resulting bias corrected Bernstein estimators as well as the additive bias corrected Bernstein estimator [Leblanc, A. (2010), 'A Bias-reduced Approach to Density Estimation Using Bernstein Polynomials', Journal of Nonparametric Statistics , 22, 459-475] are shown to be O ( n -super- - 8/9) when the underlying density has a fourth-order derivative, where n is the sample size. The condition under which the MSE near the boundary is O ( n -super- - 8/9) is also discussed. Finally, numerical studies based on both simulated and real data sets are presented.

Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://hdl.handle.net/10.1080/10485252.2013.827195 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:gnstxx:v:26:y:2014:i:1:p:61-84

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/GNST20

DOI: 10.1080/10485252.2013.827195

Access Statistics for this article

Journal of Nonparametric Statistics is currently edited by Jun Shao

More articles in Journal of Nonparametric Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().