Related papers: Minimax optimal estimators for general additive fu…
In this work, the estimation of the multivariate normal mean by different classes of shrinkage estimators is investigated. The risk associated with the balanced loss function is used to compare two estimators. We start by considering…
Standard approaches to stochastic gradient estimation, with only noisy black-box function evaluations, use the finite-difference method or its variants. While natural, it is open to our knowledge whether their statistical accuracy is the…
In this paper we will consider the estimation of a monotone regression (or density) function in a fixed point by the least squares (Grenander) estimator. We will show that this estimator is fully adaptive, in the sense that the attained…
We propose a new method for estimating the minimizer $\boldsymbol{x}^*$ and the minimum value $f^*$ of a smooth and strongly convex regression function $f$ from the observations contaminated by random noise. Our estimator $\boldsymbol{z}_n$…
We study the performance of estimators of a sparse nonrandom vector based on an observation which is linearly transformed and corrupted by additive white Gaussian noise. Using the reproducing kernel Hilbert space framework, we derive a new…
We consider the problem of estimating confidence intervals for the mean of a random variable, where the goal is to produce the smallest possible interval for a given number of samples. While minimax optimal algorithms are known for this…
This paper deals with the parametric inference for integrated signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter is multidimensional…
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…
We propose a rectangular rotational invariant estimator to recover a real matrix from noisy matrix observations coming from an arbitrary additive rotational invariant perturbation, in the large dimension limit. Using the Bayes-optimality of…
This paper addresses a problem of estimating an additive functional given $n$ i.i.d. samples drawn from a discrete distribution $P=(p_1,...,p_k)$ with alphabet size $k$. The additive functional is defined as…
The multivariate linear regression model with shuffled data and additive Gaussian noise arises in various correspondence estimation and matching problems. Focusing on the denoising aspect of this problem, we provide a characterization the…
We study minimax lower bounds for function estimation problems on large graph when the target function is smoothly varying over the graph. We derive minimax rates in the context of regression and classification problems on graphs that…
The goal of this paper is to show that a single robust estimator of the mean of a multivariate Gaussian distribution can enjoy five desirable properties. First, it is computationally tractable in the sense that it can be computed in a time…
We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower…
Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…
It is often of interest to make inference on an unknown function that is a local parameter of the data-generating mechanism, such as a density or regression function. Such estimands can typically only be estimated at a…
The computation of integrals is a fundamental task in the analysis of functional data, which are typically considered as random elements in a space of squared integrable functions. Borrowing ideas from recent advances in the Monte Carlo…
This work is intended as a contribution to a wavelet-based adaptive estimator of the memory parameter in the classical semi-parametric framework for Gaussian stationary processes. In particular we introduce and develop the choice of a…
We consider a problem of recovering a high-dimensional vector $\mu$ observed in white noise, where the unknown vector $\mu$ is assumed to be sparse. The objective of the paper is to develop a Bayesian formalism which gives rise to a family…
The effect of measurement errors in discriminant analysis is investigated. Given observations $Z=X+\epsilon$, where $\epsilon$ denotes a random noise, the goal is to predict the density of $X$ among two possible candidates $f$ and $g$. We…