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Variation Diminishing Transformations: A Direct Approach to Total Positivity and its Statistical Applications

Lawrence D. Brown, Iain M. Johnstone and K. Brenda MacGibbon
Journal of the American Statistical Association
Vol. 76, No. 376 (Dec., 1981), pp. 824-832
DOI: 10.2307/2287577
Stable URL: http://www.jstor.org/stable/2287577
Page Count: 9
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Variation Diminishing Transformations: A Direct Approach to Total Positivity and its Statistical Applications
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Abstract

Karlin has shown that the variation diminishing property possessed by totally positive distributions allows a unified and straightforward presentation of many basic properties of hypothesis tests. His work in fact reveals that total positivity is equivalent to a suitably formulated variation diminishing property. This largely expository article begins with the latter concept and consequently gives a more direct account of the theory. This approach avoids the extensive mathematical preliminaries previously required and isolates the more important statistical property.

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