Please use this identifier to cite or link to this item: https://doi.org/10.1007/s00440-004-0384-5
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dc.titleThe broken sample problem
dc.contributor.authorBai, Z.
dc.contributor.authorHsing, T.
dc.date.accessioned2014-10-28T05:15:46Z
dc.date.available2014-10-28T05:15:46Z
dc.date.issued2005-04
dc.identifier.citationBai, Z., Hsing, T. (2005-04). The broken sample problem. Probability Theory and Related Fields 131 (4) : 528-552. ScholarBank@NUS Repository. https://doi.org/10.1007/s00440-004-0384-5
dc.identifier.issn01788051
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/105410
dc.description.abstractSuppose that (X i Y i )i=12 ... n are iid. random vectors with uniform marginals and a certain joint distribution F ρ where ρ is a parameter with ρ=ρ o 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 ρ 1 and ρ 2 is impossible if the density f ρ of F ρ is square integrable and the second largest singular value of the linear operator [InlineMediaObject not available: see fulltext.] is strictly less than 1 for ρ=ρ 1 and ρ 2. We also consider this result from the perspective of a bivariate empirical process which contains information equivalent to that of the broken sample. © Springer-Verlag 2004.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1007/s00440-004-0384-5
dc.sourceScopus
dc.subjectConsistent estimation
dc.subjectEmpirical process
dc.subjectGaussian process
dc.subjectKulback-Leibler information
dc.typeArticle
dc.contributor.departmentSTATISTICS & APPLIED PROBABILITY
dc.description.doi10.1007/s00440-004-0384-5
dc.description.sourcetitleProbability Theory and Related Fields
dc.description.volume131
dc.description.issue4
dc.description.page528-552
dc.identifier.isiut000227511400004
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