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In a multiple testing problem where one is willing to tolerate a few false rejections, procedure controlling the familywise error rate (FWER) can potentially be improved in terms of its ability to detect false null hypotheses by generalizing it to control the k-FWER, the probability of falsely rejecting at least k null hypotheses, for some fixed k > 1.… (More)

- Wenge Guo, Sanat K Sarkar, Shyamal D Peddada
- Biometrics
- 2010

Microarray gene expression studies over ordered categories are routinely conducted to gain insights into biological functions of genes and the underlying biological processes. Some common experiments are time-course/dose-response experiments where a tissue or cell line is exposed to different doses and/or durations of time to a chemical. A goal of such… (More)

Results on the false discovery rate (FDR) and the false nondiscovery rate (FNR) are developed for single-step multiple testing procedures. In addition to verifying desirable properties of FDR and FNR as measures of error rates, these results extend previously known results, providing further insights, particularly under dependence, into the notions of FDR… (More)

In this work we study an adaptive step-down procedure for testing m hypotheses. It stems from the repeated use of the false discovery rate controlling the linear step-up procedure (sometimes called BH), and makes use of the critical constants iq/[(m + 1− i(1− q)], i= 1, . . . ,m. Motivated by its success as a model selection procedure, as well as by its… (More)

- Sanat K. Sarkar
- 2006

In many applications of multiple hypothesis testing where more than one false rejection can be tolerated, consideration of error rates allowing more than one, rather than at least one, false rejection can potentially increase the ability of a procedure to detect false null hypotheses. The k-FWER, which is a generalized version of the usual familywise error… (More)

- Pranab K. Sen, Sanat K. Sarkar, S. K. Sarkar
- 2008

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.

- Werner Brannath, Frank Bretz, Willi Maurer, Sanat Sarkar
- Biometrical journal. Biometrische Zeitschrift
- 2009

The two-sided Simes test is known to control the type I error rate with bivariate normal test statistics. For one-sided hypotheses, control of the type I error rate requires that the correlation between the bivariate normal test statistics is non-negative. In this article, we introduce a trimmed version of the one-sided weighted Simes test for two… (More)

Abstract. Sarkar (1998) showed that certain positively dependent (MTP2) random variables satisfy the Simes Inequality. The multivariate-t distribution does not satisfy this property, so other means are necessary to show that it also satisfies the Simes inequality. A corollary was given in Sarkar (1998) to handle this distribution, but there is an error. In… (More)

- Sanat K. Sarkar, Tianhui Zhou, Debashis Ghosh
- 2008

Abstract: A general decision theoretic formulation is given to multiple testing, allowing descriptions of measures of false discoveries and false non-discoveries in terms of certain loss functions even when randomized decisions are made on the hypotheses. Randomized as well as non-randomized procedures controlling the Bayes false discovery rate (BFDR) and… (More)

- Vishwanath Iyer, Sanat Sarkar
- Biometrical journal. Biometrische Zeitschrift
- 2007

The use of multiple hypothesis testing procedures has been receiving a lot of attention recently by statisticians in DNA microarray analysis. The traditional FWER controlling procedures are not very useful in this situation since the experiments are exploratory by nature and researchers are more interested in controlling the rate of false positives rather… (More)