Remarks on the L1 distance in statistical data analysis. Issue 19 (2nd October 2017)

• Record Type: Journal Article
• Authors: Budzyński, Robert J.; Kondracki, Witold
• Is Part Of: Communications in statistics. Volume 46:Issue 19(2017)
• Page Start: 9355
• Page End: 9363
• Publication Date: 2017-10-02
• Subjects: Histograms -- L1 distance -- univariate distributions; 62-07; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2013.799691
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: We propose the L 1 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 L 1 in the large- N limit. We argue that the L 1 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 .