Please use this identifier to cite or link to this item:
Title: The broken sample problem
Authors: Bai, Z. 
Hsing, T.
Keywords: Consistent estimation
Empirical process
Gaussian process
Kulback-Leibler information
Issue Date: Apr-2005
Citation: Bai, Z., Hsing, T. (2005-04). The broken sample problem. Probability Theory and Related Fields 131 (4) : 528-552. ScholarBank@NUS Repository.
Abstract: Suppose 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.
Source Title: Probability Theory and Related Fields
ISSN: 01788051
DOI: 10.1007/s00440-004-0384-5
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.


checked on Feb 3, 2023


checked on Feb 3, 2023

Page view(s)

checked on Feb 2, 2023

Google ScholarTM



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.