Related papers: Linear and convex aggregation of density estimator…
We consider the problem of model selection type aggregation in the context of density estimation. We first show that empirical risk minimization is sub-optimal for this problem and it shares this property with the exponential weights…
We address the problem of density estimation with $\mathbb{L}_s$-loss by selection of kernel estimators. We develop a selection procedure and derive corresponding $\mathbb{L}_s$-risk oracle inequalities. It is shown that the proposed…
Averaging provides an alternative to bandwidth selection for density kernel estimation. We propose a procedure to combine linearly several kernel estimators of a density obtained from different, possibly data-driven, bandwidths. The method…
We consider the problem of combining a (possibly uncountably infinite) set of affine estimators in non-parametric regression model with heteroscedastic Gaussian noise. Focusing on the exponentially weighted aggregate, we prove a…
We derive oracle inequalities for the problems of isotonic and convex regression using the combination of $Q$-aggregation procedure and sparsity pattern aggregation. This improves upon the previous results including the oracle inequalities…
In one-dimensional density estimation on i.i.d. observations we suggest an adaptive cross-validation technique for the selection of a kernel estimator. This estimator is both asymptotic MISE-efficient with respect to the monotone oracle,…
This paper studies statistical aggregation procedures in regression setting. A motivating factor is the existence of many different methods of estimation, leading to possibly competing estimators. We consider here three different types of…
We study the problem of nonparametric estimation under $\bL_p$-loss, $p\in [1,\infty)$, in the framework of the convolution structure density model on $\bR^d$. This observation scheme is a generalization of two classical statistical models,…
We study the problem of model selection type aggregation with respect to the Kullback-Leibler divergence for various probabilistic models. Rather than considering a convex combination of the initial estimators $f_1, \ldots, f_N$, our…
Non-linear aggregation strategies have recently been proposed in response to the problem of how to combine, in a non-linear way, estimators of the regression function (see for instance \cite{biau:16}), classification rules (see…
In this paper we study the problem of pointwise density estimation from observations with multiplicative measurement errors. We elucidate the main feature of this problem: the influence of the estimation point on the estimation accuracy. In…
This paper studies statistical aggregation procedures in the regression setting. A motivating factor is the existence of many different methods of estimation, leading to possibly competing estimators. We consider here three different types…
This paper is devoted to the estimation of the common marginal density function of weakly dependent processes. The accuracy of estimation is measured using pointwise risks. We propose a datadriven procedure using kernel rules. The bandwidth…
We consider the problem of estimating the probability density function of a circular random variable observed under censoring. To this end, we introduce a projection estimator constructed via a regression approach on linear sieves. We first…
We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant…
Aggregation methods have emerged as a powerful and flexible framework in statistical learning, providing unified solutions across diverse problems such as regression, classification, and density estimation. In the context of generalized…
We provide new general kernel selection rules thanks to penalized least-squares criteria. We derive optimal oracle inequalities using adequate concentration tools. We also investigate the problem of minimal penalty as described in [BM07].
In this paper, we investigate the almost sure convergence, in supremum norm, of the rank-based linear wavelet estimator for a multivariate copula density. Based on empirical process tools, we prove a uniform limit law for the deviation,…
We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules…
Motivated by applications in statistics and machine learning, we consider a problem of unmixing convex combinations of nonparametric densities. Suppose we observe $n$ groups of samples, where the $i$th group consists of $N_i$ independent…