Distribution of Global Measures of Deviation Between the Empirical Distribution Function and Its Concave Majorant

Vladimir N. Kulikov and Hendrik P. Lopuhaä ()
Additional contact information
Vladimir N. Kulikov: ING Financial Markets
Hendrik P. Lopuhaä: Delft University of Technology

Journal of Theoretical Probability, 2008, vol. 21, issue 2, 356-377

Abstract: Abstract We investigate the distribution of some global measures of deviation between the empirical distribution function and its least concave majorant. In the case that the underlying distribution has a strictly decreasing density, we prove asymptotic normality for several L k -type distances. In the case of a uniform distribution, we also establish their limit distribution together with that of the supremum distance. It turns out that in the uniform case, the measures of deviation are of greater order and their limit distributions are different.

Keywords: Empirical process; Least concave majorant; Central limit theorem; Brownian motion with parabolic drift; L k distance (search for similar items in EconPapers)
Date: 2008
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10959-007-0103-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:jotpro:v:21:y:2008:i:2:d:10.1007_s10959-007-0103-0

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-007-0103-0

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().