Related papers: A new method for estimating the tail index using t…

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 estimation of the extremal dependence structure is spoiled by the impact of the bias, which increases with the number of observations used for the estimation. Already known in the univariate setting, the bias correction procedure is…

Parametric stochastic simulators are ubiquitous in science, often featuring high-dimensional input parameters and/or an intractable likelihood. Performing Bayesian parameter inference in this context can be challenging. We present a neural…

There has been a surge of interest in developing robust estimators for models with heavy-tailed and bounded variance data in statistics and machine learning, while few works impose unbounded variance. This paper proposes two type of robust…

Motivated by the empirical observation of power-law distributions in the credits (e.g., ``likes'') of viral posts in social media, we introduce a high-dimensional tail index regression model and propose methods for estimation and inference…

We consider multivariate extreme value statistics for independent but nonidentically distributed random vectors. In particular, the data may have varying tail copulas and also heteroscedastic marginal distributions. Assuming smoothly…

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…

Main challenges in long-tailed recognition come from the imbalanced data distribution and sample scarcity in its tail classes. While techniques have been proposed to achieve a more balanced training loss and to improve tail classes data…

This work proposes a novel method to robustly and accurately model time series with heavy-tailed noise, in non-stationary scenarios. In many practical application time series have heavy-tailed noise that significantly impacts the…

We propose Stein-type estimators for zero-inflated Bell regression models by incorporating information on model parameters. These estimators combine the advantages of unrestricted and restricted estimators. We derive the asymptotic…

A common bottleneck in evaluating extremal performance measures is that, due to their very nature, tail data are often very limited. The conventional approach selects the best probability distribution from tail data using parametric…

To draw inference on serial extremal dependence within heavy-tailed Markov chains, Drees, Segers and Warcho{\l} [Extremes (2015) 18, 369--402] proposed nonparametric estimators of the spectral tail process. The methodology can be extended…

Empirical likelihood is a well-known nonparametric method in statistics and has been widely applied in statistical inference. The method has been employed by Lu and Peng (2002) to constructing confidence intervals for the tail index of a…

A notoriously difficult challenge in extreme value theory is the choice of the number $k\ll n$, where $n$ is the total sample size, of extreme data points to consider for inference of tail quantities. Existing theoretical guarantees for…

We consider the estimation of small probabilities or other risk quantities associated with rare but catastrophic events. In the model-based literature, much of the focus has been devoted to efficient Monte Carlo computation or analytical…

In a companion paper (McRobie(2013) arxiv:1304.3918), a simple set of `elemental' estimators was presented for the Generalized Pareto tail parameter. Each elemental estimator: involves only three log-spacings; is absolutely unbiased for all…

Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust…

This paper introduces a new classification scheme - head/tail breaks - in order to find groupings or hierarchy for data with a heavy-tailed distribution. The heavy-tailed distributions are heavily right skewed, with a minority of large…

We propose an analytical approach to the computation of tail probabilities of compound distributions whose individual components have heavy tails. Our approach is based on the contour integration method, and gives rise to a representation…

Classification on long-tailed distributed data is a challenging problem, which suffers from serious class-imbalance and accordingly unpromising performance especially on tail classes. Recently, the ensembling based methods achieve the…