Related papers: Sensitivity analysis in general metric spaces
One of the major problems for maximum likelihood estimation in the well-established directional models is that the normalising constants can be difficult to evaluate. A new general method of "score matching estimation" is presented here on…
Human-generated categorical annotations frequently produce empirical response distributions (soft labels) that reflect ambiguity rather than simple annotator error. We introduce an ambiguity measure that maps a discrete response…
This paper is mainly concerned with asymptotic studies of weighted bootstrap for u- and v-statistics. We derive the consistency of the weighted bootstrap u- and v-statistics, based on i.i.d. and non i.i.d. observations, from some more…
A new test of normality based on a standardised empirical process is introduced in this article. The first step is to introduce a Cram\'er-von Mises type statistic with weights equal to the inverse of the standard normal density function…
Statistical models incorporating change points are common in practice, especially in the area of biomedicine. This approach is appealing in that a specific parameter is introduced to account for the abrupt change in the response variable…
We introduce a flexible framework for making inferences about general linear forms of a large matrix based on noisy observations of a subset of its entries. In particular, under mild regularity conditions, we develop a universal procedure…
We give improvements of estimates of invariant metrics in the normal direction on strictly pseudoconvex domains. Specifically we will give the second term in the expansion of the metrics. This depends on an improved localisation result and…
Capability indices are dimensionless quantities measuring the aptitude of a process to manufacture items whose characteristics must be within a specified tolerance ranges. The usual indices $C_p$, $C_{pk}$, $C_{pm}$, and $C_{pmk}$ are used…
Global sensitivity analysis (GSA) can provide rich information for controlling output uncertainty. In practical applications, segmented models are commonly used to describe an abrupt model change. For segmented models, the complicated…
Hoeffding's U-statistics model combinatorial-type matrix parameters (appearing in CS theory) in a natural way. This paper proposes using these statistics for analyzing random compressed sensing matrices, in the non-asymptotic regime…
The Gauss-Bonnet Theorem is studied for edge metrics as a renormalized index theorem. These metrics include the Poincar\'e-Einstein metrics of the AdS/CFT correspondence. Renormalization is used to make sense of the curvature integral and…
The Trotter-Suzuki decomposition is one of the main approaches for realization of quantum simulations on digital quantum computers. Variance-based global sensitivity analysis (the Sobol method) is a wide used method which allows to…
Factor importance measures the impact of each feature on output prediction accuracy. Many existing works focus on the model-based importance, but an important feature in one learning algorithm may hold little significance in another model.…
In order to better fit real-world datasets, studying asymmetric distribution is of great interest. In this work, we derive several mathematical properties of a general class of asymmetric distributions with positive support which shows up…
Motivated by applications to the study of depth functions for tree-indexed random variables generated by point processes, we describe functional limit theorems for the intensity measure of point processes. Specifically, we establish uniform…
Estimating mutual information (MI) from samples is a fundamental problem in statistics, machine learning, and data analysis. Recently it was shown that a popular class of non-parametric MI estimators perform very poorly for strongly…
These lectures introduce the notion of asymptotic observables, which are classes of measurable quantities predicted by quantum field theory. In gapped theories with trivial infrared dynamics, these include scattering amplitudes, expectation…
We propose a general approach to construct weighted likelihood estimating equations with the aim of obtaining robust parameter estimates. We modify the standard likelihood equations by incorporating a weight that reflects the statistical…
Let $(X,d_X,\mu)$ be a metric measure space where $X$ is locally compact and separable and $\mu$ is a Borel regular measure such that $0 <\mu(B(x,r)) <\infty$ for every ball $B(x,r)$ with center $x \in X$ and radius $r>0$. We define…
We find a surprising link between Maz'ya-Shaposhnikova's well-known asymptotic formula concerning fractional Sobolev seminorms and the generalized Bishop-Gromov inequality. In the setting of abstract metric measure spaces we prove the…