Improved estimators of the distribution function based on lower record values

R. Arabi Belaghi (), M. Arashi and S. Tabatabaey

Statistical Papers, 2015, vol. 56, issue 2, 453-477

Abstract: In this paper, we define different types of estimators for the distribution function, namely preliminary test (PT), shrinkage PT (SPT), Stein type (S), and Thompson shrinkage (TS) estimators based on lower record observations and their inter record times. Their asymptotic distributional bias and mean square error are explicitly derived. The superiority conditions of the new proposed estimators over the existing estimator of distribution function are also obtained. It is shown that about the neighborhood of the null hypothesis $$F_0$$ F 0 , the PTE is superior to the SE in the sense of having higher asymptotic relative efficiency. Further for the reasonable values of $$\alpha $$ α the newly proposed SPT estimator uniformly dominates the non-parametric maximum like likelihood estimators in the literatures. A table is also given to be more specifics along the exhibited theoretical results for practical sake. Some graphical representations are given as proofs of our assertions. A simulation study is also carried out for some life time distribution, to examine the accuracy of the proposed estimators with a limited sample size. The results show that combination of the parametric and nonparametric estimators will give more efficient estimators. This study is finally concluded by applying the theoretic results to a real data set. Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Asymptotic distributional mean square error; Asymptotic relative efficiency; Distribution function; Local alternative; Preliminary test estimator; Record values; Stein type estimator; Primary 62H10; Secondary 62J12 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1007/s00362-014-0591-9 (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:spr:stpapr:v:56:y:2015:i:2:p:453-477

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-014-0591-9

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().