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On the Simes inequality and its generalization

Sanat K. Sarkar

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The Simes inequality has received considerable attention recently because of its close connection to some important multiple hypothesis testing procedures. We revisit in this article an old result on this inequality to clarify and strengthen it and a recently proposed generalization of it to offer an alternative simpler proof.

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N. Balakrishnan, Edsel A. Peña and Mervyn J. Silvapulle, eds., Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 231-242

First available in Project Euclid: 1 April 2008

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Primary: 62G30: Order statistics; empirical distribution functions 62H15: Hypothesis testing

multivariate totally positive of order two positive dependence through stochastic ordering probability inequalities Simes test symmetric multivariate normal symmetric multivariate t


Sarkar, Sanat K. On the Simes inequality and its generalization. Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, 231--242, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/193940307000000167.

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