Let (X, Y) be a random couple in S×T with unknown distribution P. Let (X1, Y1), …, (Xn, Yn) be i.i.d. copies of (X, Y), Pn being their empirical distribution. Let h1, …, hN:S↦[−1, 1] be a dictionary consisting of N functions. For λ∈ℝN, denote fλ:=∑j=1Nλjhj. Let ℓ:T×ℝ↦ℝ be a given loss function, which is convex with respect to the second variable. Denote (ℓ•f)(x, y):=ℓ(y; f(x)). We study the following penalized empirical risk minimization problem $${\widehat{\lambda }}^{\epsilon }:=\underset{\lambda \in {ℝ}^N}{argmin}\left[P_n(\ell •f_{\lambda })+\epsilon {\parallel \lambda \parallel }_{{\ell }_p}^p\right],$$ which is an empirical version of the problem $${\lambda }^{\epsilon }:=\underset{\lambda \in {ℝ}^N}{argmin}\left[P(\ell •f_{\lambda })+\epsilon {\parallel \lambda \parallel }_{{\ell }_p}^p\right]$$ (hereɛ≥0...

We discuss the prediction of a spatial variable of a multivariate mark composed of both dependent and explanatory variables. The marks are location-dependent and they are attached to a point process. We assume that the marks are assigned independently, conditionally on an unknown underlying parametric field. We compare (i) the classical non-parametric Nadaraya-Watson kernel estimator based on the dependent variable (ii) estimators obtained under an assumption of local parametric model where explanatory...

Given a random sample from some unknown density $f_0:ℝ\to [0,\infty )$ we devise Haar wavelet estimators for $f_0$ with variable resolution levels constructed from localised test procedures (as in Lepski, Mammen and Spokoiny (Ann. Statist.25(1997) 927–947)). We show that these estimators satisfy an oracle inequality that adapts to heterogeneous smoothness of $f_0$, simultaneously for every point $x$ in a fixed interval, in sup-norm loss. The thresholding constants involved in the test procedures can be chosen in practice under...

We consider a stationary symmetric stable bidimensional process with discrete time, having the spectral representation (1.1). We consider a general case where the spectral measure is assumed to be the sum of an absolutely continuous measure, a discrete measure of finite order and a finite number of absolutely continuous measures on several lines. We estimate the density of the absolutely continuous measure and the density on the lines.

When we apply stacked regression to classification we need only discriminant indices which can be negative. In many situations, we want these indices to be positive, e.g., if we want to use them to count posterior probabilities, when we want to use stacked regression to combining classification. In such situation, we have to use leastsquares regression under the constraint βₖ ≥ 0, k = 1,2,...,K. In their earlier work [5], LeBlanc and Tibshirani used an algorithm given in [4]. However, in this paper...

One of the most widely-used multivariate conditional volatility models is the dynamic conditional correlation (or DCC) specification. However, the underlying stochastic process to derive DCC has not yet been established, which has made problematic the derivation of asymptotic properties of the Quasi-Maximum Likelihood Estimators (QMLE). To date, the statistical properties of the QMLE of the DCC parameters have purportedly been derived under highly restrictive and unverifiable regularity conditions....

Given a realization on a finite interval of a continuous-time stationary process, we construct estimators for higher order spectral densities. Tapering and shift-in-time methods are used to build estimators which are asymptotically unbiased and consistent for all admissible values of the argument. Asymptotic results for the fourth-order densities are given. Detailed attention is paid to the nth order case.

This article presents a new concept for a statistical fault detection system, including the detection, diagnosis, and prediction of faults. Theoretical material has been collected to provide a complete algorithm making possible the design of a usable system for statistical inference on the basis of the current value of a symptom vector. The use of elements of artificial intelligence enables self-correction and adaptation to changing conditions. The mathematical apparatus is founded on the methodology...


Many protein sequences present non trivial periodicities, such as cysteine signatures and leucine heptads. These known periodicities probably represent a small percentage of the total number of sequences periodic structures, and it is useful to have general tools to detect such sequences and their period in large databases of sequences. We compare three statistics adapted from those used in time series analysis: a generalisation of the simple autocovariance based on a similarity score and two statistics...

Many protein sequences present non trivial periodicities, such as cysteine signatures and leucine heptads. These known periodicities probably represent a small percentage of the total number of sequences periodic structures, and it is useful to have general tools to detect such sequences and their period in large databases of sequences. We compare three statistics adapted from those used in time series analysis: a generalisation of the simple autocovariance based on a similarity score and two statistics...

Unbiased risk estimation, à la Stein, is studied for infinitely divisible laws with finite second moment.

The prediction of size extremes in Wicksell’s corpuscle problem with oblate spheroids is considered. Three-dimensional particles are represented by their planar sections (profiles) and the problem is to predict their extremal size under the assumption of a constant shape factor. The stability of the domain of attraction of the size extremes is proved under the tail equivalence condition. A simple procedure is proposed of evaluating the normalizing constants from the tail behaviour of appropriate...

The stress-strength model is proposed based on the $m$-generalized order statistics and the corresponding concomitant. For the dependency between $m$-generalized order statistics and its concomitant, a bivariate copula expansion is considered and the stress-strength model is obtained for two special cases of order statistics and upper record values. In the particular case of copula function, the generalized Farlie-Gumbel-Morgenstern bivariate distribution function is considered with proportional reversed...