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https://doi.org/10.1007/s00440-004-0384-5
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. https://doi.org/10.1007/s00440-004-0384-5 | 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 | URI: | http://scholarbank.nus.edu.sg/handle/10635/105410 | ISSN: | 01788051 | DOI: | 10.1007/s00440-004-0384-5 |
Appears in Collections: | Staff Publications |
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