 Estimation of the quantile function using Bernstein-Durrmeyer polynomialsA. Pepelyshev, E. Rafajłowicz and A. Steland Journal of Nonparametric Statistics, 2014, vol. 26, issue 1, 1-20 Abstract: This paper studies quantile estimation using Bernstein-Durrmeyer polynomials in terms of its mean squared error and integrated mean squared error including rates of convergence as well as its asymptotic distribution. Whereas the rates of convergence are achieved for i.i.d. samples, we also show that the consistency more or less directly follows from the consistency of the sample quantiles, such that our proposal can also be applied for risk measurement in finance and insurance. Furthermore, an improved estimator based on an error-correction approach is proposed for which a general consistency result is established. A crucial issue is how to select the degree of Bernstein-Durrmeyer polynomials. We propose a novel data-adaptive approach that controls the number of modes of the corresponding density estimator. Its consistency including an uniform error bound as well as its limiting distribution in the sense of a general invariance principle are established. The finite sample properties are investigated by a Monte Carlo study. Finally, the results are illustrated by an application to photovoltaic energy research. Date: 2014 Downloads: (external link) Related works: 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:1-20 Ordering information: This journal article can be ordered from DOI: 10.1080/10485252.2013.826355 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 |
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