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The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a large collection of possible covariates from which we hope to select a parsimonious set for the efficient prediction of a… (More)

Microarrays are a novel technology that facilitates the simultaneous measurement of thousands of gene expression levels. A typical microarray experiment can produce millions of data points, raising serious problems of data reduction, and simultaneous inference. We consider one such experiment in which oligonucleotide arrays were employed to assess the… (More)

Current scientific techniques in genomics and image processing routinely produce hypothesis testing problems with hundreds or thousands of cases to consider simultaneously. This poses new difficulties for the statistician, but also opens new opportunities. In particular it allows empirical estimation of an appropriate null hypothesis. The empirical null may… (More)

- Bradley Efron, Robert Tibshirani, Bradley EFRONand, Robert TIBSHIRANI
- 2007

Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Each copy of any part of a JSTOR transmission must contain the same copyright notice that… (More)

This paper discusses the problem of identifying differentially expressed groups of genes from a microarray experiment. The groups of genes are externally defined, for example, sets of gene pathways derived from biological databases. Our starting point is the interesting Gene Set Enrichment Analysis (GSEA) procedure of Subramanian et al. (2005). We study the… (More)

This article surveys bootstrap methods for producing good approximate confidence intervals. The goal is to improve by an order of magnitude upon the accuracy of the standard intervalsˆθ ± z α ˆ σ, in a way that allows routine application even to very complicated problems. Both theory and examples are used to show how this is done. The first seven sections… (More)

- B Efron, R Tibshirani
- Science
- 1991

Most of our familiar statistical methods, such as hypothesis testing, linear regression, analysis of variance, and maximum likelihood estimation, were designed to be implemented on mechanical calculators. Modern electronic computation has encouraged a host of new statistical methods that require fewer distributional assumptions than their predecessors and… (More)

- Bradley Efron, Robert Tibshirani
- Genetic epidemiology
- 2002

In a classic two-sample problem, one might use Wilcoxon's statistic to test for a difference between treatment and control subjects. The analogous microarray experiment yields thousands of Wilcoxon statistics, one for each gene on the array, and confronts the statistician with a difficult simultaneous inference situation. We will discuss two inferential… (More)

- Bradley Efron
- 2004

Having constructed a data-based estimation rule, perhaps a logistic regression or a classification tree, the statistician would like to know its performance as a predictor of future cases. There are two main theories concerning prediction error: (1) penalty methods such as C p , AIC, and SURE that depend on the covariance between data points and their… (More)

- Bradley Efron
- 2006

Large-scale hypothesis testing problems, with hundreds or thousands of test statistics " z i " to consider at once, have become familiar in current practice. Applications of popular analysis methods such as false discovery rate techniques do not require independence of the z i 's, but their accuracy can be compromised in high-correlation situations. This… (More)