Related papers: Adaptive Dantzig density estimation
The paper deals with the density estimation on Rd under sup- norm loss. We provide with fully data-driven estimation procedure and establish for it so called sup-norm oracle inequality. The pro- posed estimator allows to take into account…
We exhibit an approximate equivalence between the Lasso estimator and Dantzig selector. For both methods we derive parallel oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the…
We discuss the problem of adaptive discrete-time signal denoising in the situation where the signal to be recovered admits a "linear oracle" -- an unknown linear estimate that takes the form of convolution of observations with a…
In many applications one may acquire a composition of several signals that may be corrupted by noise, and it is a challenging problem to reliably separate the components from one another without sacrificing significant details. Adding to…
Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…
We consider the linear regression problem, where the number $p$ of covariates is possibly larger than the number $n$ of observations $(x_{i},y_{i})_{i\leq i \leq n}$, under sparsity assumptions. On the one hand, several methods have been…
In this paper we present new theoretical results for the Dantzig and Lasso estimators of the drift in a high dimensional Ornstein-Uhlenbeck model under sparsity constraints. Our focus is on oracle inequalities for both estimators and error…
Neural network-based methods for (un)conditional density estimation have recently gained substantial attention, as various neural density estimators have outperformed classical approaches in real-data experiments. Despite these empirical…
In this paper we consider the problem of estimating $f$, the conditional density of $Y$ given $X$, by using an independent sample distributed as $(X,Y)$ in the multivariate setting. We consider the estimation of $f(x,.)$ where $x$ is a…
The theory of adaptive estimation and oracle inequalities for the case of Gaussian-shift--finite-interval experiments has made significant progress in recent years. In particular, sharp-minimax adaptive estimators and exact exponential-type…
This paper develops a general theory for first-order descent methods whose search directions are restricted to a prescribed dictionary in a reflexive Banach space. Instead of assuming that the linear span of the dictionary is dense, as in…
This paper presents a novel approach for pointwise estimation of multivariate density functions on known domains of arbitrary dimensions using nonparametric local polynomial estimators. Our method is highly flexible, as it applies to both…
Regression problems are traditionally analyzed via univariate characteristics like the regression function, scale function and marginal density of regression errors. These characteristics are useful and informative whenever the association…
Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function.…
We study the distribution of the adaptive LASSO estimator (Zou (2006)) in finite samples as well as in the large-sample limit. The large-sample distributions are derived both for the case where the adaptive LASSO estimator is tuned to…
Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges…
In the present paper we consider application of overcomplete dictionaries to solution of general ill-posed linear inverse problems. In the context of regression problems, there has been enormous amount of effort to recover an unknown…
We prove concentration inequalities and associated PAC bounds for continuous- and discrete-time additive functionals for possibly unbounded functions of multivariate, nonreversible diffusion processes. Our analysis relies on an approach via…
The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density…
We give oracle inequalities on procedures which combines quantization and variable selection via a weighted Lasso $k$-means type algorithm. The results are derived for a general family of weights, which can be tuned to size the influence of…