Assessment of the reliability of various types of equipment relies on statistical inference about characteristics of reliability such as reliability function, mean lifetime of the devices, or failure rate. General techniques of statistical inference (estimation and hypotheses testing) are reviewed in Estimation; Least-Squares Estimation; Maximum Likelihood; Nonparametric Tests; Hypothesis Testi...

In a classical parametric setup, a key factor in the implementation of the Empirical Bayes methodology is the incorporation of a suitable prior that is compatible with the parametric setup and yet lends to the estimation of the Bayes (shrinkage) factor in an empirical manner. The situation is more complex in semi-parametric and (ev,:,n more in) nonparametric models. Although the Dirichlet prior...

The Cp selection criterion is a popular method to choose the smoothing parameter in spline regression. Another widely used method is the generalized maximum likelihood (GML) derived from a normal-theory empirical Bayes framework. These two seemingly unrelated methods, have been shown in Efron (Ann. Statist. 29 (2001) 470) and Kou and Efron (J. Amer. Statist. Assoc. 97 (2002) 766) to be actually...

We consider a joint processing of n independent sparse regression problems. Each is based on a sample (yi1, xi1) . . . , (yim, xim) of m i.i.d. observations from yi1 = x T i1βi+εi1, yi1 ∈ R, xi1 ∈ R, i = 1, . . . , n, and εi1 ∼ N(0, σ), say. p is large enough so that the empirical risk minimizer is not consistent. We consider three possible extensions of the lasso estimator to deal with this pr...

cDNA microarrays are used in many contexts to compare mRNA levels between samples of cells. Microarray experiments typically give us expression measurements on 1000-20 000 genes, but with few replicates for each gene. Traditional methods using means and standard deviations to detect differential expression are not satisfactory in this context. A handful of alternative statistics have been devel...