Related papers: Optimal inference for the mean of random functions
We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly…
We provide an upper bound as a random variable for the functions of estimators in high dimensions. This upper bound may help establish the rate of convergence of functions in high dimensions. The upper bound random variable may converge…
The problem of optimally measuring an analytic function of unknown local parameters each linearly coupled to a qubit sensor is well understood, with applications ranging from field interpolation to noise characterization. Here, we resolve a…
Adaptive estimation of a quadratic functional over both Besov and $L_p$ balls is considered. A collection of nonquadratic estimators are developed which have useful bias and variance properties over individual Besov and $L_p$ balls. An…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
We study estimation of a multivariate function $f:{\bf R}^d \to {\bf R}$ when the observations are available from function $Af$, where $A$ is a known linear operator. Both the Gaussian white noise model and density estimation are studied.…
This paper concerns the estimation of the regression function at a given point in nonparametric heteroscedastic models with Gaussian noise or with noise having unknown distribution. In the two cases an asymptotically efficient kernel…
Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…
This article investigates nonparametric estimation of variance functions for functional data when the mean function is unknown. We obtain asymptotic results for the kernel estimator based on squared residuals. Similar to the finite…
Let $A:[0,1]\rightarrow\mathbb{H}_m$ (the space of Hermitian matrices) be a matrix valued function which is low rank with entries in H\"{o}lder class $\Sigma(\beta,L)$. The goal of this paper is to study statistical estimation of $A$ based…
In this paper, we propose a novel approach to fit a functional linear regression in which both the response and the predictor are functions of a common variable such as time. We consider the case that the response and the predictor…
Consider the design based situation where an $r$-regular set is sampled on a random lattice. A fast algorithm for estimating the integrated mean curvature based on this observation is to use a weighted sum of $2\times \dotsm \times 2$…
This paper deals with a nonparametric shape respecting estimation method for U-shaped or unimodal functions. A general upper bound for the nonasymptotic L_1-risk of the estimator is given. The method is applied to the shape respecting…
We consider the estimation of two-sample integral functionals, of the type that occur naturally, for example, when the object of interest is a divergence between unknown probability densities. Our first main result is that, in wide…
We provide a novel characterization of semiparametric efficiency in a generic supervised learning setting where the outcome mean function -- defined as the conditional expectation of the outcome of interest given the other observed…
In this paper we propose an optimal predictor of a random variable that has either an infinite mean or an infinite variance. The method consists of transforming the random variable such that the transformed variable has a finite mean and…
We propose a new procedure for inference on optimal treatment regimes in the model-free setting, which does not require to specify an outcome regression model. Existing model-free estimators for optimal treatment regimes are usually not…
We study estimation of a multivariate function $f:\mathbf{R}^d\to\mathbf{R}$ when the observations are available from the function $Af$, where $A$ is a known linear operator. Both the Gaussian white noise model and density estimation are…
In the nonparametric regression setting, we construct an estimator which is a continuous function interpolating the data points with high probability, while attaining minimax optimal rates under mean squared risk on the scale of H\"older…
We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set $\mathcal{G}$ up to the smallest possible additive term, called the convergence rate. When the…