Specific Gaussian mixtures are considered to solve simultaneously variable selection and clustering problems. A non asymptotic penalized criterion is proposed to choose the number of mixture components and the relevant variable subset. Because of the non linearity of the associated Kullback-Leibler contrast on Gaussian mixtures, a general model selection theorem for maximum likelihood estimation proposed by [Massart Concentration inequalities and model selection Springer, Berlin (2007). Lectures...

Specific Gaussian mixtures are considered to solve simultaneously variable selection and clustering problems. A non asymptotic penalized criterion is proposed to choose the number of mixture components and the relevant variable subset. Because of the non linearity of the associated Kullback-Leibler contrast on Gaussian mixtures, a general model selection theorem for maximum likelihood estimation proposed by [Massart Concentration inequalities and model selection Springer, Berlin (2007). Lectures...

The author applies the test criterion of P. Rothety to the statistical analysis of the positive correclation of symmetric pairs of observations. In this particular case he arrives at some new results. His work ends with a general proof of the consistency of Rothery's test.

We consider the problem of simultaneous testing of a finite number of null hypotheses $H_i$, i=1,...,s. Starting from the classical paper of Lehmann (1957), it has become a very popular subject of research. In many applications, particularly in molecular biology (see e.g. Dudoit et al. (2003), Pollard et al. (2005)), the number s, i.e. the number of tested hypotheses, is large and the popular procedures that control the familywise error rate (FWERM) have small power. Therefore, we are concerned with...

We present a first moment distribution-free bound on expected values of L-statistics as well as properties of some numerical characteristics of order statistics, in the case when the observations are possibly dependent symmetrically distributed about the common mean. An actuarial interpretation of the presented bound is indicated.

The problem of nonparametric estimation of the regression function f(x) = E(Y | X=x) using the orthonormal system of trigonometric functions or Legendre polynomials $e_k$, k=0,1,2,..., is considered in the case where a sample of i.i.d. copies $(X_i,Y_i)$, i=1,...,n, of the random variable (X,Y) is available and the marginal distribution of X has density ϱ ∈ $L^1$[a,b]. The constructed estimators are of the form ${\widehat{f}}_n\left(x\right)={\sum }_{k=0}^{N\left(n\right)}{\widehat{c}}_k{e}_k\left(x\right)$, where the coefficients ${\widehat{c}}_0,{\widehat{c}}_1,...,{\widehat{c}}_N$ are determined by minimizing the empirical risk $n^{-1}{\sum }_{i=1}^n{(Y_i-{\sum }_{k=0}^N{c}_k{e}_k\left(X_i\right))}^2$. Sufficient conditions for...

Let $\left\{X_n\right\}$ be a stationary and ergodic time series taking values from a finite or countably infinite set $𝒳$ and that $f\left(X\right)$ is a function of the process with finite second moment. Assume that the distribution of the process is otherwise unknown. We construct a sequence of stopping times ${\lambda }_n$ along which we will be able to estimate the conditional expectation $E\left(f\left(X_{{\lambda }_n+1}\right)\right|X_0,\cdots ,X_{{\lambda }_n})$ from the observations $(X_0,\cdots ,X_{{\lambda }_n})$ in a point wise consistent way for a restricted class of stationary and ergodic finite or countably infinite alphabet time series...

Computationally attractive Fisher consistent robust estimation methods based on adaptive explanatory variables trimming are proposed for the logistic regression model. Results of a Monte Carlo experiment and a real data analysis show its good behavior for moderate sample sizes. The method is applicable when some distributional information about explanatory variables is available.

In this note we consider the estimation of the differential entropy of a probability density function. We propose a new adaptive estimator based on a plug-in approach and wavelet methods. Under the mean ${𝕃}_p$ error, $p\ge 1$, this estimator attains fast rates of convergence for a wide class of functions. We present simulation results in order to support our theoretical findings.