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Bias reduction in tail estimation has received considerable interest in extreme value analysis. Estimation methods that minimize the bias while keeping the mean squared error (MSE) under control, are especially useful when applying…

Statistics Theory · Mathematics 2016-06-21 Gaonyalelwe Maribe , Andréhette Verster , Jan Beirlant

This work studies applications and generalizations of a simple estimation technique that provides exponential concentration under heavy-tailed distributions, assuming only bounded low-order moments. We show that the technique can be used…

Machine Learning · Computer Science 2016-04-19 Daniel Hsu , Sivan Sabato

We investigate the application of the Adaptive Multilevel Splitting algorithm for the estimation of tail probabilities of solutions of Stochastic Differential Equations evaluated at a given time, and of associated temporal averages. We…

Probability · Mathematics 2019-03-27 Charles-Edouard Bréhier , Tony Lelièvre

The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the…

Methodology · Statistics 2014-05-27 Ioannis Papastathopoulos , Jonathan A. Tawn

In this paper we present an enhancement of the regression-based variance reduction approaches recently proposed in Belomestny et al. This enhancement is based on a truncation of the control variate and allows for a significant reduction of…

Probability · Mathematics 2017-11-10 Denis Belomestny , Stefan Häfner , Mikhail Urusov

This paper studies the distributed optimization problem under the influence of heavy-tailed gradient noises. Here, a heavy-tailed noise means that the noise does not necessarily satisfy the bounded variance assumption. Instead, it satisfies…

Optimization and Control · Mathematics 2025-05-12 Chao Sun , Huiming Zhang , Bo Chen , Li Yu

We obtain in this paper a non-asymptotic non-improvable up to multiplicative constant moment and exponential tail estimates for distribution for U-statistics by means of martingale representation. We show also the exactness of obtained…

Statistics Theory · Mathematics 2016-02-02 E. Ostrovsky , L. Sirota

Traditional quantile estimators that are based on one or two order statistics are a common way to estimate distribution quantiles based on the given samples. These estimators are robust, but their statistical efficiency is not always good…

Methodology · Statistics 2022-08-30 Andrey Akinshin

In this paper, based on the kernel estimator proposed by Ould-Said and Lemdani (Ann. Instit. Statist. Math. 2006), we develop some new generalized M-estimator procedures for single index regression models with left-truncated responses. The…

Statistics Theory · Mathematics 2018-01-22 Kong Lingtao , Zhang Yanli , Dai Hongshuai

We study inference on the common stochastic trends in a non-stationary, $N$-variate time series $y_{t}$, in the possible presence of heavy tails. We propose a novel methodology which does not require any knowledge or estimation of the tail…

Econometrics · Economics 2021-07-30 Matteo Barigozzi , Giuseppe Cavaliere , Lorenzo Trapani

We use Stein characterisations to derive new moment-type estimators for the parameters of several truncated multivariate distributions in the i.i.d. case; we also derive the asymptotic properties of these estimators. Our examples include…

Statistics Theory · Mathematics 2024-06-18 Adrian Fischer , Robert E. Gaunt , Yvik Swan

The drift sequential parameter estimation problems for the Cox-Ingersoll-Ross (CIR) processes under the limited duration of observation are studied. Truncated sequential estimation methods for both scalar and {two}-dimensional parameter…

Statistics Theory · Mathematics 2025-04-08 Mohamed Ben Alaya , Thi-Bao Trâm Ngô , Serguei Pergamenchtchikov

We derive in this short report the exponential as well as power decreasing tail estimations for the sums of centered exchangeable random variables, alike ones for the sums of the centered independent ones.

Probability · Mathematics 2022-06-02 M. R. Formica , E. Ostrovsky , L. Sirota

Recently, long-tailed image classification harvests lots of research attention, since the data distribution is long-tailed in many real-world situations. Piles of algorithms are devised to address the data imbalance problem by biasing the…

Computer Vision and Pattern Recognition · Computer Science 2023-02-06 Chaowei Fang , Dingwen Zhang , Wen Zheng , Xue Li , Le Yang , Lechao Cheng , Junwei Han

Recent algebraic parametric estimation techniques led to point-wise derivative estimates by using only the iterated integral of a noisy observation signal. In this paper, we extend such differentiation methods by providing a larger choice…

Numerical Analysis · Mathematics 2011-03-04 Da-Yan Liu , Olivier Gibaru , Wilfrid Perruquetti

For purposes of Value-at-Risk estimation, we consider several multivariate families of heavy-tailed distributions, which can be seen as multidimensional versions of Paretian stable and Student's t distributions allowing different marginals…

Risk Management · Quantitative Finance 2011-12-20 Carlo Marinelli , Stefano d'Addona , Svetlozar T. Rachev

Asmussen and Lehtomaa [Distinguishing log-concavity from heavy tails. Risks 5(10), 2017] introduced an interesting function $g$ which is able to distinguish between log-convex and log-concave tail behaviour of distributions, and proposed a…

Methodology · Statistics 2023-07-25 Toshiya Iwashita , Bernhard Klar

We derive a novel variational expectation maximization approach based on truncated posterior distributions. Truncated distributions are proportional to exact posteriors within subsets of a discrete state space and equal zero otherwise. The…

Machine Learning · Statistics 2019-07-12 Jörg Lücke

We derive the sharp non-asymptotical uniform estimations for tails of distributions for classical normed sums of centered normed independent random vectors having a moderate decreasing individual tails of summands.

Probability · Mathematics 2021-10-08 M. R. Formica , E. Ostrovsky , L. Sirota

We study the problem of estimating the parameters of a Gaussian distribution when samples are only shown if they fall in some (unknown) subset $S \subseteq \R^d$. This core problem in truncated statistics has long history going back to…

Statistics Theory · Mathematics 2019-08-06 Vasilis Kontonis , Christos Tzamos , Manolis Zampetakis