Related papers: Nonparametric estimation over shrinking neighborho…
Learning kernels in operators from data lies at the intersection of inverse problems and statistical learning, providing a powerful framework for capturing non-local dependencies in function spaces and high-dimensional settings. In contrast…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
Driven by a wide range of applications, many principal subspace estimation problems have been studied individually under different structural constraints. This paper presents a unified framework for the statistical analysis of a general…
This paper continues the research started in \cite{LW16}. In the framework of the convolution structure density model on $\bR^d$, we address the problem of adaptive minimax estimation with $\bL_p$--loss over the scale of anisotropic…
The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the…
This paper aims first at a simultaneous axiomatic presentation of the proof of optimal convergence rates for adaptive finite element methods and second at some refinements of particular questions like the avoidance of (discrete) lower…
We study location-scale mixture priors for nonparametric statistical problems, including multivariate regression, density estimation and classification. We show that a rate-adaptive procedure can be obtained if the prior is properly…
The semiparametric regression models have attracted increasing attention owing to their robustness compared to their parametric counterparts. This paper discusses the efficiency bound for functional response models (FRM), an emerging class…
Given a dictionary of $M_n$ initial estimates of the unknown true regression function, we aim to construct linearly aggregated estimators that target the best performance among all the linear combinations under a sparse $q$-norm ($0 \leq q…
This paper studies a Bayesian approach to non-asymptotic minimax adaptation in nonparametric estimation. Estimating an input function on the basis of output functions in a Gaussian white-noise model is discussed. The input function is…
Given observations from a circular random variable contaminated by an additive measurement error, we consider the problem of minimax optimal goodness-of-fit testing in a non-asymptotic framework. We propose direct and indirect testing…
We consider the problem of locating a jump discontinuity (change-point) in a smooth parametric regression model with a bounded covariate. It is assumed that one can sample the covariate at different values and measure the corresponding…
In many statistical and econometric applications, we gather individual samples from various interconnected populations that undeniably exhibit common latent structures. Utilizing a model that incorporates these latent structures for such…
The development of wavelet theory has in recent years spawned applications in signal processing, in fast algorithms for integral transforms, and in image and function representation methods. This last application has stimulated interest in…
We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the…
A distributed adaptive algorithm to estimate a time-varying signal, measured by a wireless sensor network, is designed and analyzed. One of the major features of the algorithm is that no central coordination among the nodes needs to be…
Majority-vote ensembles achieve variance reduction by averaging over diverse, approximately independent base learners. When training data exhibits Markov dependence, as in time-series forecasting, reinforcement learning (RL) replay buffers,…
This paper studies adaptive sensing for estimating the nonzero amplitudes of a sparse signal with the aim of providing analytical guarantees on the performance gain due to adaptive resource allocation. We consider a previously proposed…
Bayesian error analysis paves the way to the construction of credible and plausible error regions for a point estimator obtained from a given dataset. We introduce the concept of region accuracy for error regions (a generalization of the…
Empirical research typically involves a robustness-efficiency tradeoff. A researcher seeking to estimate a scalar parameter can invoke strong assumptions to motivate a restricted estimator that is precise but may be heavily biased, or they…