Remarks on the L1 distance in statistical data analysis

Robert J. Budzyński and Witold Kondracki

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 19, 9355-9363

Abstract: We propose the L1 distance between the distribution of a binned data sample and a probability distribution from which it is hypothetically drawn as a statistic for testing agreement between the data and a model. We study the distribution of this distance for N-element samples drawn from k bins of equal probability and derive asymptotic formulae for the mean and dispersion of L1 in the large-N limit. We argue that the L1 distance is asymptotically normally distributed, with the mean and dispersion being accurately reproduced by asymptotic formulae even for moderately large values of N and k.

Date: 2017
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2013.799691 (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:lstaxx:v:46:y:2017:i:19:p:9355-9363

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20

DOI: 10.1080/03610926.2013.799691

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().