English
Related papers

Related papers: Adaptive and minimax optimal estimation of the tai…

200 papers

We consider the problem setting of prediction with expert advice with possibly heavy-tailed losses, i.e. the only assumption on the losses is an upper bound on their second moments, denoted by $\theta$. We develop adaptive algorithms that…

Machine Learning · Computer Science 2026-01-09 Antoine Moulin , Emmanuel Esposito , Dirk van der Hoeven

We present a nonparametric family of estimators for the tail index of a Pareto-type distribution when covariate information is available. Our estimators are based on a weighted sum of the log-spacings between some selected observations.…

Statistics Theory · Mathematics 2011-04-06 L. Gardes , S. Girard

In the world of multivariate extremes, estimation of the dependence structure still presents a challenge and an interesting problem. A procedure for the bivariate case is presented that opens the road to a similar way of handling the…

Statistics Theory · Mathematics 2008-11-14 John H. J. Einmahl , Andrea Krajina , Johan Segers

A $d$-dimensional nonparametric additive regression model with dependent observations is considered. Using the marginal integration technique and wavelets methodology, we develop a new adaptive estimator for a component of the additive…

Statistics Theory · Mathematics 2012-08-07 Christophe Chesneau , Jalal M. Fadili , Bertrand Maillot

Bilevel optimization minimizes an objective function, defined by an upper-level problem whose feasible region is the solution of a lower-level problem. We study the oracle complexity of finding an $\epsilon$-stationary point with…

Optimization and Control · Mathematics 2025-12-01 Lesi Chen , Jingzhao Zhang

Recently some papers, such as Aban, Meerschaert and Panorska (2006), Nuyts (2010) and Clark (2013), have drawn attention to possible truncation in Pareto tail modelling. Sometimes natural upper bounds exist that truncate the probability…

Statistics Theory · Mathematics 2015-05-21 Jan Beirlant , Isabel Fraga Alves , Ivette Gomes

Given $n$ samples from a population of individuals belonging to different species, what is the number $U$ of hitherto unseen species that would be observed if $\lambda n$ new samples were collected? This is an important problem in many…

Statistics Theory · Mathematics 2022-03-17 Stefano Favaro , Zacharie Naulet

Ratios of central order statistics seem to be very useful for estimating the tail of the distributions and therefore, quantiles outside the range of the data. In 1995 Isabel Fraga Alves investigated the rate of convergence of three…

Statistics Theory · Mathematics 2021-02-03 Pavlina K. Jordanova , Milan Stehlí k

The relationship between a response variable and its covariates can vary significantly, especially in scenarios where covariates take on extremely high or low values. This paper introduces a max-linear tail regression model specifically…

Methodology · Statistics 2025-02-24 Liujun Chen , Deyuan Li , Zhengjun Zhang

We propose a class of weighted least squares estimators for the tail index of a distribution function with a regularly varying upper tail. Our approach is based on the method developed by \cite{Holan2010} for the Parzen tail index.…

Statistics Theory · Mathematics 2020-03-02 Amenah AL-Najafi , László Viharos

In the framework of nonparametric multivariate function estimation we are interested in structural adaptation. We assume that the function to be estimated has the "single-index" structure where neither the link function nor the index vector…

Statistics Theory · Mathematics 2013-04-30 Oleg Lepski , Nora Serdyukova

In the framework of nonparametric multivariate function estimation we are interested in structural adaptation. We assume that the function to be estimated possesses the single-index structure where neither the link function nor the index…

Statistics Theory · Mathematics 2013-04-26 Oleg Lepski , Nora Serdyukova

We study methods for aggregating pairwise comparison data in order to estimate outcome probabilities for future comparisons among a collection of n items. Working within a flexible framework that imposes only a form of strong stochastic…

Machine Learning · Computer Science 2016-03-23 Nihar B. Shah , Sivaraman Balakrishnan , Martin J. Wainwright

We estimate convex polytopes and general convex sets in $\mathbb R^d,d\geq 2$ in the regression framework. We measure the risk of our estimators using a $L^1$-type loss function and prove upper bounds on these risks. We show that, in the…

Statistics Theory · Mathematics 2012-11-16 Victor-Emmanuel Brunel

This work proposes a universal and adaptive second-order method for minimizing second-order smooth, convex functions. Our algorithm achieves $O(\sigma / \sqrt{T})$ convergence when the oracle feedback is stochastic with variance $\sigma^2$,…

Optimization and Control · Mathematics 2022-12-13 Kimon Antonakopoulos , Ali Kavis , Volkan Cevher

Nonparametric estimation of nonlocal interaction kernels is crucial in various applications involving interacting particle systems. The inference challenge, situated at the nexus of statistical learning and inverse problems, arises from the…

Statistics Theory · Mathematics 2025-04-24 Xiong Wang , Inbar Seroussi , Fei Lu

We study a new estimator for the tail index of a distribution in the Frechet domain of attraction that arises naturally by computing subsample maxima. This estimator is equivalent to taking a U-statistic over a Hill estimator with two order…

Methodology · Statistics 2015-03-20 Stefan Wager

In this paper, we consider the problem of the estimation of a Weibull tail-coefficient. In particular, we propose a regression model, from which we derive a bias-reduced estimator. This estimator is based on a least-squares approach. The…

Statistics Theory · Mathematics 2011-04-01 J. Diebolt , L. Gardes , S. Girard , A. Guillou

We study nonasymptotic minimax estimation of the linear functional $L(\theta)=\eta^\top \theta$ for a high-dimensional $s$-sparse mean vector with an arbitrary loading vector $\eta$. For symmetric noise with exponentially decaying tails, we…

Statistics Theory · Mathematics 2026-04-29 Jie Xie , Dongming Huang

In this paper we continue the investigation of the SRCEN estimator of the extreme value index $\gamma$ (or the tail index $\alpha=1/\gamma$) proposed in \cite{MCE} for $\gamma>1/2$. We propose a new estimator based on the local maximum.…

Statistics Theory · Mathematics 2017-10-10 Natalia Markovich , Marijus Vaičiulis