Related papers: Nonparametric Confidence Regions for Level Sets: S…

This paper considers the distributed computation of confidence regions tethered to multidimensional parameter estimation under linear measurement models. In particular, the considered confidence regions are non-asymptotic, this meaning that…

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…

The problem of constructing confidence regions for the median in the nonparametric measurement error model (NMEM) is considered. This problem arises in many settings, including inference about the median lifetime of a complex system arising…

We study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces, and illustrate their use…

We present nonparametric techniques for constructing and verifying density estimates from high-dimensional data whose irregular dependence structure cannot be modelled by parametric multivariate distributions. A low-dimensional…

Vertically weighted averages perform a bilateral filtering of data, in order to preserve fine details of the underlying signal, especially discontinuities such as jumps (in dimension one) or edges (in dimension two). In homogeneous regions…

We investigate and extend the conformal prediction method due to Vovk,Gammerman and Shafer (2005) to construct nonparametric prediction regions. These regions have guaranteed distribution free, finite sample coverage, without any…

Filamentary structures, also called ridges, generalize the concept of modes of density functions and provide low-dimensional representations of point clouds. Using kernel type plug-in estimators, we give asymptotic confidence regions for…

Nonparametric density estimators are studied for $d$-dimensional, strongly spatial mixing data which is defined on a general $N$-dimensional lattice structure. We consider linear and nonlinear hard thresholded wavelet estimators which are…

Data analysis in high-dimensional spaces aims at obtaining a synthetic description of a data set, revealing its main structure and its salient features. We here introduce an approach providing this description in the form of a topography of…

Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for…

We describe a general method for the construction of a confidence region for the two parameters of the Negative Binomial Distribution. This is achieved by expanding the sampling distribution of Method-of-Moments estimators, using the…

Psychometrics and quantitative psychology rely strongly on statistical models to measure psychological processes. As a branch of mathematics, geometry is inherently connected to measurement and focuses on properties such as distance and…

Precision matrices play important roles in many practical applications. Motivated by temporally dependent multivariate data in modern social and scientific studies, we consider the statistical inference of precision matrices for…

We propose a new inferential framework for constructing confidence regions and testing hypotheses in statistical models specified by a system of high dimensional estimating equations. We construct an influence function by projecting the…

We present a geometric method to determine confidence sets for the ratio E(Y)/E(X) of the means of random variables X and Y. This method reduces the problem of constructing confidence sets for the ratio of two random variables to the…

We build confidence balls for the common density $s$ of a real valued sample $X_1,...,X_n$. We use resampling methods to estimate the projection of $s$ onto finite dimensional linear spaces and a model selection procedure to choose an…

In the setting of high-dimensional linear regression models, we propose two frameworks for constructing pointwise and group confidence sets for penalized estimators which incorporate prior knowledge about the organization of the non-zero…

In this paper, we develop nonparametric inference on spatial regression models as an extension of Lu and Tj\ostheim(2014), which develops nonparametric inference on density functions of stationary spatial processes under domain expanding…

We consider the problem of constructing robust nonparametric confidence intervals and tests of hypothesis for the median when the data distribution is unknown and the data may contain a small fraction of contamination. We propose a…