We say that a distribution over {0, 1} is ( , k)-wise independent if its restriction to every k coordinates results in a distribution that is -close to the uniform distribution. A natural question regarding ( , k)-wise independent distributions is how close they are to some k-wise independent distribution. We show that there exists ( , k)-wise independent distribution whose statistical distance...

The microarray gene expression applications have greatly stimulated the statistical research on the massive multiple hypothesis tests problem. There is now a large body of literature in this area and basically five paradigms of massive multiple tests: control of the false discovery rate (FDR), estimation of FDR, significance threshold criteria, control of family-wise error rate (FWER) or genera...

Joshua N. Sampson, Simina M. Boca, Steven C. Moore, and Ruth Heller Division of Cancer Epidemiology and Genetics, National Cancer Institute, Rockville, MD, US, [email protected] Innovation Center for Biomedical Informatics, Georgetown University, Washington, DC, US, [email protected] Division of Cancer Epidemiology and Genetics, National Cancer Institute, Rockville, MD, US, steven.moor...

1 Prliminaries 2 1.1 Basic Probability concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Stochastic Differential Equations (SDE’s) . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 Langevin equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.2 Ito integral and basics of Ito calculus . . . . . . . . . . . . . . ....

We present a novel method for controlling the k-familywise error rate (k-FWER) in the linear regression setting using the knockoffs framework first introduced by Barber and Candès. Our procedure, which we also refer to as knockoffs, can be applied with any design matrix with at least as many observations as variables, and does not require knowing the noise variance. Unlike other multiple testin...

Multiple comparison procedures that control a family-wise error rate or false discovery rate provide an achieved error rate as the adjusted p-value or q-value for each hypothesis tested. However, since achieved error rates are not understood as probabilities that the null hypotheses are true, empirical Bayes methods have been employed to estimate such posterior probabilities, called local false...

Multiple hypothesis testing is a significant problem in nearly all neuroimaging studies. In order to correct for this phenomena, we require a reliable estimate of the Family-Wise Error Rate (FWER). The well known Bonferroni correction method, while being simple to implement, is quite conservative, and can substantially under-power a study because it ignores dependencies between test statistics....

Air pollution is considered by many researchers to be one of the causes global warming, with detrimental effects on environment, economy, and society. Therefore, identifying roles some possible factors for air an important research agenda. To this end, using unbalanced panel data, study endeavours explore globalization, technological innovation renewable energy in thus improving quality world’s...