Related papers: Gaussian approximation to the extreme value index …

In this paper, we consider the problem of estimating an extreme quantile of a Weibull tail-distribution. The new extreme quantile estimator has a reduced bias compared to the more classical ones proposed in the literature. It is based on an…

We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a non-asymptotic point of view. In particular, we define estimators with a…

Higher criticism is a large-scale testing procedure that can attain the optimal detection boundary for sparse and faint signals. However, there has been a lack of knowledge in most existing works about its asymptotic distribution for more…

This article proposes a new method of truncated estimation to estimate the tail index $\alpha$ of the extremely heavy-tailed distribution with infinite mean or variance. We not only present two truncated estimators $\hat{\alpha}$ and…

In extreme value analysis, the extreme value index plays a vital role as it determines the tail heaviness of the underlying distribution and is the primary parameter required for the estimation of other extreme events. In this paper, we…

Simulation from the truncated multivariate normal distribution in high dimensions is a recurrent problem in statistical computing, and is typically only feasible using approximate MCMC sampling. In this article we propose a minimax tilting…

The dominant approaches to text representation in natural language rely on learning embeddings on massive corpora which have convenient properties such as compositionality and distance preservation. In this paper, we develop a novel method…

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.

We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…

The well-known Koml\'os-Major-Tusn\'ady inequalities [Z. Wahrsch. Verw. Gebiete 32 (1975) 111-131; Z. Wahrsch. Verw. Gebiete 34 (1976) 33-58] provide sharp inequalities to partial sums of iid standard exponential random variables by a…

Kaplan-Meier and Nelson-Aalen integral estimators to the tail index of right-censored Pareto-type data traditionally rely on the assumption that the proportion p of upper uncensored observations exceeds one-half, corresponding to weak…

We present new estimators of the mean of a real valued random variable, based on PAC-Bayesian iterative truncation. We analyze the non-asymptotic minimax properties of the deviations of estimators for distributions having either a bounded…

A wide range of natural and social phenomena result in observables whose distributions can be well approximated by a power-law decay. The well-known Hill estimator of the tail exponent provides results which are in many respects superior to…

We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…

We consider the fitting of heavy tailed data and distribution with a special attention to distributions with a non--standard shape in the "body" of the distribution. To this end we consider a dense class of heavy tailed distributions…

In this paper we present a novel methodology to perform Bayesian model selection in linear models with heavy-tailed distributions. We consider a finite mixture of distributions to model a latent variable where each component of the mixture…

Consider $n$ i.i.d. random vectors on $\mathbb{R}^2$, with unknown, common distribution function $F$. Under a sharpening of the extreme value condition on $F$, we derive a weighted approximation of the corresponding tail copula process.…

In this paper we study the asymptotic behavior of the Gaussian quasi maximum likelihood estimator of a stationary GARCH process with heavy-tailed innovations. This means that the innovations are regularly varying with index…

We address the estimation of quantiles from heavy-tailed distributions when functional covariate information is available and in the case where the order of the quantile converges to one as the sample size increases. Such "extreme"…

This study develops a non-asymptotic Gaussian approximation theory for distributions of M-estimators, which are defined as maximizers of empirical criterion functions. In existing mathematical statistics literature, numerous studies have…