Related papers: On discrimination between two close distribution t…
For the basic case of $L_2$ optimal transport between two probability measures on a Euclidean space, the regularity of the coupling measure and the transport map in the tail regions of these measures is studied. For this purpose, Robert…
This paper develops a smooth test of goodness-of-fit for elliptical distributions. The test is adaptively omnibus, invariant to affine-linear transformations and has a convenient expression that can be broken into components. These…
We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on $L^2$-distances of the empirical zero-bias transformation to the normal distribution or the empirical…
We introduce a new characterization of the Cauchy distribution and propose a class of goodness-of-fit tests to the Cauchy family. The limit distribution is derived in a Hilbert space framework under the null hypothesis and under fixed…
There are a number of mathematical formalisms of the term "outlier" in statistics, though there is no consensus on what the right notion ought to be. Accordingly, we try to give a consistent and robust definition for a specific type of…
We call two copulas tail equivalent if their first-order approximations in the tail coincide. As a special case, a copula is called tail symmetric if it is tail equivalent to the associated survival copula. We propose a novel measure and…
The directed preferential attachment model is revisited. A new exact characterization of the limiting in- and out-degree distribution is given by two \emph{independent} pure birth processes that are observed at a common exponentially…
A general and relatively simple method for construction of multivariate goodness-of-fit tests is introduced. The proposed test is applied to elliptical distributions. The method is based on a characterization of probability distributions…
We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we…
We consider distinguishing between two distribution tail models when tails of one model are lighter (or heavier) than those of the other. Two procedures are proposed: one scale-free and one location- and scale-free, and their asymptotic…
A new distribution is introduced, which we call the twin-t distribution. This distribution is heavy-tailed like the t distribution, but closer to normality in the central part of the curve. Its properties are described, e.g. the pdf, the…
This paper establishes the functional convergence of the Extreme Nelson--Aalen and Extreme Kaplan--Meier estimators, which are designed to capture the heavy-tailed behaviour of censored losses. The resulting limit representations can be…
A novel statistical method is proposed and investigated for estimating a heavy tailed density under mild smoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the…
We consider heavy-tailed distributions and compare the well-known estimators of the tail index, based on extreme value theory with a comparatively recent estimator based on a different idea.
In this article, we introduce a novel discrepancy called the maximum variance discrepancy for the purpose of measuring the difference between two distributions in Hilbert spaces that cannot be found via the maximum mean discrepancy. We also…
We propose a goodness-of-fit test for the distribution of errors from a multivariate indirect regression model. The test statistic is based on the Khmaladze transformation of the empirical process of standardized residuals. This…
We study the problem of discrete distribution testing in the two-party setting. For example, in the standard closeness testing problem, Alice and Bob each have $t$ samples from, respectively, distributions $a$ and $b$ over $[n]$, and they…
In samples from a heavy-tailed distribution a second-order approximation is often use to approximate the tail function. Based on the parameters of the approximation, an optimal sample fraction can be estimated which is then used to estimate…
It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and…
The upper tail of a claim size distribution of a property line of business is frequently modelled by Pareto distribution. However, the upper tail does not need to be Pareto distributed, extraordinary shapes are possible. Here, the…