Related papers: Confidence regions for excursion sets in asymptoti…
We give an overview of the recent asymptotic results on the geometry of excursion sets of stationary random fields. Namely, we cover a number of limit theorems of central type for the volume of excursions of stationary (quasi--, positively…
Image analysis frequently deals with shape estimation and image reconstruction. The ob jects of interest in these problems may be thought of as random sets, and one is interested in finding a representative, or expected, set. We consider a…
Motivated by the questions of risk assessment in climatology (temperature change in North America) and medicine (impact of statin usage and COVID-19 on hospitalized patients), we address the problem of estimating the set in the domain of a…
We propose a methodology for constructing confidence regions with partially identified models of general form. The region is obtained by inverting a test of internal consistency of the econometric structure. We develop a dilation bootstrap…
We study the asymptotic frequentist coverage of credible sets based on a novel Bayesian approach for a multiple linear regression model under variable selection. We initially ignore the issue of variable selection, which allows us to put a…
The asymptotic results pertaining to the distribution of the log likelihood ratio allow for the creation of a confidence region, which is a general extension of the confidence interval. Two and three dimensional regions can be displayed…
The excursion set of a $C^2$ smooth random field carries relevant information in its various geometric measures. From a computational viewpoint, one never has access to the continuous observation of the excursion set, but rather to…
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…
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…
In this paper, we introduce a targeted exploration strategy for the non-asymptotic, finite-time case. The proposed strategy is applicable to uncertain linear time-invariant systems subject to sub-Gaussian disturbances. As the main result,…
We focus on the construction of confidence corridors for multivariate nonparametric generalized quantile regression functions. This construction is based on asymptotic results for the maximal deviation between a suitable nonparametric…
This paper addresses the problem of detecting and estimating the anisotropy of a stationary real-valued random field from a single realization of one of its excursion sets. This setting is challenging as it relies on observing a binary…
We develop a fast and accurate grouped penalized credible region approach for variable selection and prediction in Bayesian high-dimensional linear regression. Most existing Bayesian methods either are subject to high computational costs…
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…
The problem of quantifying uncertainty about the locations of multiple change points by means of confidence intervals is addressed. The asymptotic distribution of the change point estimators obtained as the local maximisers of moving sum…
Environmental sensors are crucial for monitoring weather conditions and the impacts of climate change. However, it is challenging to place sensors in a way that maximises the informativeness of their measurements, particularly in remote…
Consider the observation of n iid realizations of an experiment with d>1 possible outcomes, which corresponds to a single observation of a multinomial distribution M(n,p) where p is an unknown discrete distribution on {1,...,d}. In many…
Robust design has been widely recognized as a leading method in reducing variability and improving quality. Most of the engineering statistics literature mainly focuses on finding "point estimates" of the optimum operating conditions for…
Asymptotic uniform confidence bands are constructed for a multivariate nonparametric regression model with heteroscedastic noise, employing histogram estimators under flexible partition conditions. The construction is especially applicable…
The Peaks Over Threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is a rich applied literature on Bayesian inference for the POT, the asymptotic theory for such proposals…