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The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…

In this paper, a novel approach to the problem of estimating the heavy-tail exponent alpha>0 of a distribution is proposed. It is based on the fact that block-maxima of size m of the independent and identically distributed data scale at a…

Statistics Theory · Mathematics 2007-06-13 Stilian A. Stoev , George Michailidis , Murad S. Taqqu

We consider fluctuations of error terms $\Delta(x)$ appearing in the asymptotic formula for a summatory function of coefficients of the Dirichlet series. These are quantified via $\Omega$ and $\Omega_{\pm}$ estimates. We obtain $\Omega$…

Number Theory · Mathematics 2018-07-27 Kamalakshya Mahatab , Anirban Mukhopadhyay

Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…

Machine Learning · Statistics 2023-06-16 Feynman Liang , Liam Hodgkinson , Michael W. Mahoney

The Dirichlet distribution, also known as multivariate beta, is the most used to analyse frequencies or proportions data. Maximum likelihood is widespread for estimation of Dirichlet's parameters. However, for small sample sizes, the…

Methodology · Statistics 2021-03-04 Vincenzo Gioia , Euloge Clovis Kenne Pagui

We consider the problem of meta-analyzing two-group studies that report the median of the outcome. Often, these studies are excluded from meta-analysis because there are no well-established statistical methods to pool the difference of…

Methodology · Statistics 2022-06-22 Sean McGrath , Hojoon Sohn , Russell Steele , Andrea Benedetti

Adaptive experiments are becoming increasingly popular in real-world applications for effectively maximizing in-sample welfare and efficiency by data-driven sampling. Despite their growing prevalence, however, the statistical foundations…

Statistics Theory · Mathematics 2026-04-15 Ziang Niu , Zhimei Ren

Several techniques exist to assess and reduce nonresponse bias, including propensity models, calibration methods, or post-stratification. These approaches can only be applied after the data collection, and assume reliable information…

Methodology · Statistics 2020-05-26 Blanka Szeitl , Tamás Rudas

A novel and comprehensive methodology designed to tackle the challenges posed by extreme values in the context of random censorship is introduced. The main focus is on the analysis of integrals based on the product-limit estimator of…

Statistics Theory · Mathematics 2025-02-18 Martin Bladt , Igor Rodionov

When optimizing against the mean loss over a distribution of predictions in the context of a regression task, then even if there is a distribution of targets the optimal prediction distribution is always a delta function at a single value.…

Machine Learning · Computer Science 2019-02-11 Nicholas Guttenberg

We consider a multidimensional diffusion X with drift coefficient b({\alpha},X(t)) and diffusion coefficient {\epsilon}{\sigma}({\beta},X(t)). The diffusion is discretely observed at times t_k=k{\Delta} for k=1..n on a fixed interval [0,T].…

Statistics Theory · Mathematics 2013-05-17 Romain Guy , Catherine Laredo , Elisabeta Vergu

Estimating the tail index parameter is one of the primal objectives in extreme value theory. For heavy-tailed distributions the Hill estimator is the most popular way to estimate the tail index parameter. Improving the Hill estimator was…

Methodology · Statistics 2018-06-05 László Németh , András Zempléni

This paper investigates pooling strategies for tail index and extreme quantile estimation from heavy-tailed data. To fully exploit the information contained in several samples, we present general weighted pooled Hill estimators of the tail…

Statistics Theory · Mathematics 2021-11-08 Abdelaati Daouia , Simone A. Padoan , Gilles Stupfler

The block maxima method is a classical and widely applied statistical method for time series extremes. It has recently been found that respective estimators whose asymptotics are driven by empirical means can be improved by using sliding…

Statistics Theory · Mathematics 2023-08-29 Axel Bücher , Torben Staud

In this article, we develop a framework to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the limits of spherical integrals obtained in [46,47]. As examples, we obtain 1. a…

Probability · Mathematics 2023-04-25 Serban Belinschi , Alice Guionnet , Jiaoyang Huang

In numerous regular statistical models, median bias reduction (Kenne Pagui et al., 2017) has proven to be a noteworthy improvement over maximum likelihood, alternative to mean bias reduction. The estimator is obtained as solution to a…

Methodology · Statistics 2020-12-01 Euloge Clovis Kenne Pagui , Alessandra Salvan , Nicola Sartori

Conventional test-time adaptation (TTA) approaches typically adapt the model using only a small fraction of test samples, often those with low-entropy predictions, thereby failing to fully leverage the available information in the test…

Computer Vision and Pattern Recognition · Computer Science 2026-04-21 Nam Nguyen Phuong , Duc Nguyen The Minh , Phi Le Nguyen , Ehsan Abbasnejad , Minh Hoai

Recently, the concept of tail dependence has been discussed in financial applications related to market or credit risk. The multivariate extreme value theory is a proper tool to measure and model dependence, for example, of large loss…

Applications · Statistics 2011-09-27 Marta Ferreira

Consider the task of generating samples from a tilted distribution of a random vector whose underlying distribution is unknown, but samples from it are available. This finds applications in fields such as finance and climate science, and in…

Determinantal point processes (DPPs) have become a significant tool for recommendation systems, feature selection, or summary extraction, harnessing the intrinsic ability of these probabilistic models to facilitate sample diversity. The…

Machine Learning · Statistics 2020-07-09 Rémi Bardenet , Subhroshekhar Ghosh