The species abundance distribution and the total number of species are fundamental descriptors of the biodiversity of an ecological community. This paper focuses on situations where large numbers of rare species are not observed in the data set due to insufficient sampling of the community, as...

The bias of the empirical error rate in supervised classification is studied. It is shown that this bias can be understood as a covariance between the classification rule and the labeling of the training data. From this result, a new penalized criterion is proposed to perform model selection in...

In this paper, the problem of variable selection in classification is considered. On the basis of recent developments in model selection theory, we provide a criterion based on penalized empirical risk, where the penalization explicitly takes into account the number of variables of the...

In microarray experiments, accurate estimation of the gene variance is a key step in the identification of differentially expressed genes. Variance models go from the too stringent homoscedastic assumption to the overparameterized model assuming a specific variance for each gene. Between these...

Let (Xn)n[greater-or-equal, slanted]1 be a sequence of real random variables. The local score is Hn=max1[less-than-or-equals, slant]i<j[less-than-or-equals, slant]n (Xi+...+Xj). If (Xn)n[greater-or-equal, slanted]1 is a "good" Markov chain under its invariant measure, the Xi are centered, we prove that converges in distribution to B1* when n-->+[infinity], where B1*=max0[less-than-or-equals, slant]u[less-than-or-equals, slant]1 Bu and (Bu,u[greater-or-equal, slanted]0) is a standard Brownian motion,...</j[less-than-or-equals,>