NDLI: The broken sample problem

Content Provider	Springer Nature Link
Author	Bai, Zhidong Hsing, Tailen
Copyright Year	2004
Abstract	Suppose that (Xi,Yi),i=1,2, ... ,n, are iid. random vectors with uniform marginals and a certain joint distribution Fρ, where ρ is a parameter with ρ=ρo corresponds to the independence case. However, the X’s and Y’s are observed separately so that the pairing information is missing. Can ρ be consistently estimated? This is an extension of a problem considered in (1980) which focused on the bivariate normal distribution with ρ being the correlation. In this paper we show that consistent discrimination between two distinct parameter values ρ1 and ρ2 is impossible if the density fρ of Fρ is square integrable and the second largest singular value of the linear operator is strictly less than 1 for ρ=ρ1 and ρ2. We also consider this result from the perspective of a bivariate empirical process which contains information equivalent to that of the broken sample.
Starting Page	528
Ending Page	552
Page Count	25
File Format	PDF
ISSN	01788051
Journal	Probability Theory and Related Fields
Volume Number	131
Issue Number	4
e-ISSN	14322064
Language	English
Publisher	Springer-Verlag
Publisher Date	2004-09-12
Publisher Place	Berlin/Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Consistent estimation Empirical process Gaussian process Kulback-Leibler information Mathematical Biology in General Quantitative Finance Probability Theory and Stochastic Processes Mathematical and Computational Physics Statistics for Business/Economics/Mathematical Finance/Insurance Operation Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Analysis Statistics, Probability and Uncertainty

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