Related papers: Independent Approximates provide a maximum likelih…
Many real-world prediction tasks have outcome variables that have characteristic heavy-tail distributions. Examples include copies of books sold, auction prices of art pieces, demand for commodities in warehouses, etc. By learning…
We study the fundamental task of outlier-robust mean estimation for heavy-tailed distributions in the presence of sparsity. Specifically, given a small number of corrupted samples from a high-dimensional heavy-tailed distribution whose mean…
A tail empirical process for heavy-tailed and right-censored data is introduced and its Gaussian approximation is established. In this context, a (weighted) new Hill-type estimator for positive extreme value index is proposed and its…
Estimating extreme quantiles is an important task in many applications, including financial risk management and climatology. More important than estimating the quantile itself is to insure zero coverage error, which implies the quantile…
We present an overview of possible reasons for the appearance of heavy-tailed distributions in applications to the natural sciences. These distributions include the laws of Pareto, Lotka, and some new ones. The reasons are illustrated using…
Empirical-likelihood-based confidence intervals for a mean were introduced by Owen [Biometrika 75 (1988) 237-249], where at least a finite second moment is required. This excludes some important distributions, for example, those in the…
Let $(X_n:n\geq 0)$ be a sequence of i.i.d. r.v.'s with negative mean. Set $S_0=0$ and define $S_n=X_1+... +X_n$. We propose an importance sampling algorithm to estimate the tail of $M=\max \{S_n:n\geq 0\}$ that is strongly efficient for…
Heavy tailed phenomena are naturally analyzed by extreme value statistics. A crucial step in such an analysis is the estimation of the extreme value index, which describes the tail heaviness of the underlying probability distribution. We…
Both parametric distribution functions appearing in extreme value theory - the generalized extreme value distribution and the generalized Pareto distribution - have log-concave densities if the extreme value index gamma is in [-1,0].…
We characterize the existence of the maximum likelihood estimator for discrete exponential families. Our criterion is simple to apply as we show in various settings, most notably for exponential models of random graphs. As an application,…
A weighted Gaussian approximation to tail product-limit process for Pareto-like distributions of randomly right-truncated data is provided and a new consistent and asymptotically normal estimator of the extreme value index is derived. A…
In this paper non-asymptotic exponential and moment estimates are derived for tail of distribution for discrete time martingale under norming sequence 1/n, as in the classical Law of Large Numbers (LLN), by means of martingale differences…
The Generalized Pareto Distribution (GPD) plays a central role in modelling heavy tail phenomena in many applications. Applying the GPD to actual datasets however is a non-trivial task. One common way suggested in the literature to…
In this paper, we introduce reduced-bias estimators for the estimation of the tail index of a Pareto-type distribution. This is achieved through the use of a regularised weighted least squares with an exponential regression model for…
We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample…
In extreme value inference it is a fundamental problem how the target value is required to be extreme by the extreme value theory. In iid settings this study both theoretically and numerically compares tail estimators, which are based on…
The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the…
Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the…
We investigate a way of comparing and classifying tails of random variables. Our approach extends the notion of classical indices, such as exponential and moment indices, which are widely used measuring heaviness of tail functions. A…
Many management decisions involve accumulated random realizations for which only the first and second moments of their distribution are available. The sharp Chebyshev-type bound for the tail probability and Scarf bound for the expected loss…