Related papers: Adaptive estimation in the nonparametric random co…
In this paper, we study the problem of adaptive estimation of the spectral density of a stationary Gaussian process. For this purpose, we consider a wavelet-based method which combines the ideas of wavelet approximation and estimation by…
We estimate convex polytopes and general convex sets in $\mathbb R^d,d\geq 2$ in the regression framework. We measure the risk of our estimators using a $L^1$-type loss function and prove upper bounds on these risks. We show that, in the…
We develop our previous works concerning the identification of the collection of significant factors determining some, in general, non-binary random response variable. Such identification is important, e.g., in biological and medical…
In the present paper we consider the problem of estimating a periodic $(r+1)$-dimensional function $f$ based on observations from its noisy convolution. We construct a wavelet estimator of $f$, derive minimax lower bounds for the $L^2$-risk…
We introduce new method for generating correlated or uncorrelated Bernoulli random variables by using the binary expansion of a continuous random variable with support on the unit interval. We show that when this variable has a symmetric…
We consider testing for presence of a signal in Gaussian white noise with intensity 1/sqrt(n), when the alternatives are given by smoothness ellipsoids with an L2-ball of (squared) radius rho removed. It is known that, for a fixed Sobolev…
We consider a binary sequence generated by thresholding a hidden continuous sequence. The hidden variables are assumed to have a compound symmetry covariance structure with a single parameter characterizing the common correlation. We study…
We study the Besov regularity of wavelet series on $\mathbb{R}^d$ with randomly chosen coefficients. More precisely, each coefficient is a product of a random factor and a parameterized deterministic factor (decaying with the scale $j$ and…
In this work we propose an adaptive multilevel version of subset simulation to estimate the probability of rare events for complex physical systems. Given a sequence of nested failure domains of increasing size, the rare event probability…
We analyze the performance of alternating minimization for loss functions optimized over two variables, where each variable may be restricted to lie in some potentially nonconvex constraint set. This type of setting arises naturally in…
In statistical exercises where there are several candidate models, the traditional approach is to select one model using some data driven criterion and use that model for estimation, testing and other purposes, ignoring the variability of…
Discrete ordinal responses such as Likert scales are regularly proposed in questionnaires and used as dependent variable in modeling. The response distribution for such scales is always discrete, with bounded support and often skewed. In…
We observe a random measure $N$ and aim at estimating its intensity $s$. This statistical framework allows to deal simultaneously with the problems of estimating a density, the marginals of a multivariate distribution, the mean of a random…
The sample compression theory provides generalization guarantees for predictors that can be fully defined using a subset of the training dataset and a (short) message string, generally defined as a binary sequence. Previous works provided…
This paper studies the estimation of the conditional density f (x, $\times$) of Y i given X i = x, from the observation of an i.i.d. sample (X i , Y i) $\in$ R d , i = 1,. .. , n. We assume that f depends only on r unknown components with…
This paper provides a new methodology to analyze unobserved heterogeneity when observed characteristics are modeled nonlinearly. The proposed model builds on varying random coefficients (VRC) that are determined by nonlinear functions of…
We put forward an adaptive alpha (Type I Error) that decreases as the information grows, for hypothesis tests in which nested linear models are compared. A less elaborate adaptation was already presented in \citet{PP2014} for comparing…
This paper considers extensions of minimum-disparity estimators to the problem of estimating parameters in a regression model that is conditionally specified; that is where a parametric model describes the distribution of a response $y$…
We study the Cox models with semiparametric relative risk, which can be partially linear with one nonparametric component, or multiple additive or nonadditive nonparametric components. A penalized partial likelihood procedure is proposed to…
When randomized ensembles such as bagging or random forests are used for binary classification, the prediction error of the ensemble tends to decrease and stabilize as the number of classifiers increases. However, the precise relationship…