Related papers: Confidence balls in Gaussian regression
In this paper we propose a general methodology, based on multiple testing, for testing that the mean of a Gaussian vector in R^n belongs to a convex set. We show that the test achieves its nominal level, and characterize a class of vectors…
Post-data statistical inference concerns making probability statements about model parameters conditional on observed data. When a priori knowledge about parameters is available, post-data inference can be conveniently made from Bayesian…
The paper considers so-called adaptive estimations of regression, distribution density and spectral density of a Gaussian stationary sequence, asymptotically optimal in order at a growing number of observation on any regular subspace…
We prove the large-dimensional Gaussian approximation of a sum of $n$ independent random vectors in $\mathbb{R}^d$ together with fourth-moment error bounds on convex sets and Euclidean balls. We show that compared with classical…
We derive non-asymptotic confidence regions for the mean of a random vector whose coordinates have an unknown dependence structure. The random vector is supposed to be either Gaussian or to have a symmetric bounded distribution, and we…
We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking…
We develop a general framework for conducting inference on the mean of dependent random variables given constraints on their dependency graph. We establish the consistency of an oracle variance estimator of the mean when the dependency…
We present an estimator of the covariance matrix $\Sigma$ of random $d$-dimensional vector from an i.i.d. sample of size $n$. Our sole assumption is that this vector satisfies a bounded $L^p-L^2$ moment assumption over its one-dimensional…
3D Gaussian Splatting enables high-quality real-time rendering but often produces millions of splats, resulting in excessive storage and computational overhead. We propose a novel lossy compression method based on learnable confidence…
The presented paper is devoted to statistical modeling of Gaussian scalar real random fields inside a three-dimensional sphere (ball). We propose a statistical model describing the spatial heterogeneity in a unit ball and a numerical…
This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If…
A central result in statistical theory is Pinsker's theorem, which characterizes the minimax rate in the normal means model of nonparametric estimation. In this paper, we present an extension to Pinsker's theorem where estimation is carried…
This work investigates application of different machine learning based prediction methodologies to estimate the performance of silicon based textured cells. Concept of confidence bound regions is introduced and advantages of this concept…
We study the problem of learning a high-density region of an arbitrary distribution over $\mathbb{R}^d$. Given a target coverage parameter $\delta$, and sample access to an arbitrary distribution $D$, we want to output a confidence set $S…
Reacting against the limitation of statistics to decision procedures, R. A. Fisher proposed for inductive reasoning the use of the fiducial distribution, a parameter-space distribution of epistemological probability transferred directly…
Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…
Uniform asymptotic confidence bands for a multivariate regression function in an inverse regression model with a convolution-type operator are constructed. The results are derived using strong approximation methods and a limit theorem for…
When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generalized) fiducial inference, etc. fall under this umbrella. This…
In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive point estimation, the…
We propose a way to construct fiducial distributions for a multidimensional parameter using a step-by-step conditional procedure related to the inferential importance of the components of the parameter. For discrete models, in which the…