相关论文: On the efficiency of Gini's mean difference
An inequality is derived for the average $t$-energy of pinned distance measures, where $0 < t < 1$. This refines Mattila's theorem on distance sets to pinned distance sets, and gives an analogue of Liu's theorem for pinned distance sets of…
The main goal of this paper is to provide a brief survey of recent results which connect together results from different areas of research. It is well known that numerical integration of functions with mixed smoothness is closely related to…
This paper presents findings from a web-experiment on a representative sample of the French population. It examines the acceptability of the Pigou-Dalton principle of transfers, which posits that transferring income from an individual to a…
We discuss some properties of the distance functions on Riemannian manifolds and we relate their behavior to the geometry of the manifolds. This leads to alternative proofs of some "classical" theorems connecting curvature and topology.
In systematic reviews and meta-analysis, researchers often pool the results of the sample mean and standard deviation from a set of similar clinical trials. A number of the trials, however, reported the study using the median, the minimum…
We provide a general method for evaluation of the joint range of f-divergences for two different functions f. Via topological arguments we prove that the joint range for general distributions equals the convex hull of the joint range…
We compute bias, variance, and approximate confidence intervals for the efficiency of a random selection process under various special conditions that occur in practical data analysis. We consider the following cases: a) the number of…
The problem of estimating the mean of random functions based on discretely sampled data arises naturally in functional data analysis. In this paper, we study optimal estimation of the mean function under both common and independent designs.…
We develop a framework for generalized variational inference in infinite-dimensional function spaces and use it to construct a method termed Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance between Gaussian…
Discrepancy measures between probability distributions are at the core of statistical inference and machine learning. In many applications, distributions of interest are supported on different spaces, and yet a meaningful correspondence…
We bound the mean distance in a connected graph which is not a tree in function of its order $n$ and its girth $g$. On one hand, we show that mean distance is at most $\frac{n+1}{3}-\frac{g(g^2-4)}{12n(n-1)}$ if $g$ is even and at most…
Measuring the distance between data points is fundamental to many statistical techniques, such as dimension reduction or clustering algorithms. However, improvements in data collection technologies has led to a growing versatility of…
The goal of this note is to present a modification of the popular median of means estimator that achieves sub-Gaussian deviation bounds with nearly optimal constants under minimal assumptions on the underlying distribution. We build on a…
This note points out how confidence interval estimates for standard deviation transform into confidence interval estimates for the power of F-tests at fixed alternative means. An application is shown for the test of a two-sided hypothesis…
Nearest neighbor methods have become popular in official statistics, mainly in imputation or in statistical matching problems; they play a key role in machine learning too, where a high number of variants have been proposed. The choice of…
We show that an almost trivial inequality for the first and second mean of a random variable can be used to give non-trivial improvements on deep results. As applications we improve on results on lower bounds for the Riemann zeta-function…
Defining a distance in a mixed setting requires the quantification of observed differences of variables of different types and of variables that are measured on different scales. There exist several proposals for mixed variable distances,…
In the paper, the monotonicity and logarithmic convexity of Gini means and related functions are investigated.
We study a generalization of the Fr\'echet mean on metric spaces, which we call $\phi$-means. Our generalization is indexed by a convex function $\phi$. We find necessary and sufficient conditions for $\phi$-means to be finite and provide a…
We consider the Gittins index for a normal distribution with unknown mean $\theta$ and known variance where $\theta$ has a normal prior. In addition to presenting some monotonicity properties of the Gittins index, we derive an approximation…