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In this paper, we propose an estimator of the second-order parameter of randomly right-truncated Pareto-type distributions data and establish its consistency and asymptotic normality. Moreover, we derive an asymptotically unbiased estimator…

Statistics Theory · Mathematics 2016-10-21 Nawel Haouas , Abdelhakim Necir , Brahim Brahimi

Learning probabilistic models over strings is an important issue for many applications. Spectral methods propose elegant solutions to the problem of inferring weighted automata from finite samples of variable-length strings drawn from an…

Machine Learning · Computer Science 2013-12-24 François Denis , Mattias Gybels , Amaury Habrard

We provide a necessary and sufficient condition for the ratio of two jointly alpha-Frechet random variables to be regularly varying. This condition is based on the spectral representation of the joint distribution and is easy to check in…

Statistics Theory · Mathematics 2011-02-04 Yizao Wang

Tail dependence models for distributions attracted to a max-stable law are fitted using observations above a high threshold. To cope with spatial, high-dimensional data, a rank-based M-estimator is proposed relying on bivariate margins…

Methodology · Statistics 2015-01-12 John Einmahl , Anna Kiriliouk , Andrea Krajina , Johan Segers

We study an equivalence of (i) deterministic pathwise statements appearing in the online learning literature (termed \emph{regret bounds}), (ii) high-probability tail bounds for the supremum of a collection of martingales (of a specific…

Probability · Mathematics 2015-10-15 Alexander Rakhlin , Karthik Sridharan

This paper extends classical probabilistic results to the broader class of demimartingales and demisubmartingales. We establish variants of Doob's-type optional sampling theorem under minimal structural conditions on stopping times, relying…

Probability · Mathematics 2025-07-24 Milto Hadjikyriakou , B. L. S Prakasa Rao

We study concentration inequalities for structured weighted sums of random data, including (i) tensor inner products and (ii) sequential matrix sums. We are interested in tail bounds and concentration inequalities for those structured…

Statistics Theory · Mathematics 2026-02-11 Chen Cheng , Rina Foygel Barber

We propose and analyze TRAiL (Tangential Randomization in Linear Bandits), a computationally efficient regret-optimal forced exploration algorithm for linear bandits on action sets that are sublevel sets of strongly convex functions. TRAiL…

Machine Learning · Statistics 2024-11-20 Arda Güçlü , Subhonmesh Bose

We study finite-armed semiparametric bandits, where each arm's reward combines a linear component with an unknown, potentially adversarial shift. This model strictly generalizes classical linear bandits and reflects complexities common in…

Machine Learning · Statistics 2025-06-18 Seok-Jin Kim , Gi-Soo Kim , Min-hwan Oh

We study the problem of constructing honest and adaptive confidence intervals for the tail coefficient in the second order Pareto model, when the second order coefficient is unknown. This problem is translated into a testing problem on the…

Statistics Theory · Mathematics 2014-09-18 Alexandra Carpentier , Arlene K. H. Kim

We propose a novel approach to concentration for non-independent random variables. The main idea is to ``pretend'' that the random variables are independent and pay a multiplicative price measuring how far they are from actually being…

Information Theory · Computer Science 2023-10-31 Amedeo Roberto Esposito , Marco Mondelli

Thompson sampling (TS) is one of the most popular and earliest algorithms to solve stochastic multi-armed bandit problems. We consider a variant of TS, named $\alpha$-TS, where we use a fractional or $\alpha$-posterior ($\alpha\in(0,1)$)…

Machine Learning · Statistics 2023-09-13 Prateek Jaiswal , Debdeep Pati , Anirban Bhattacharya , Bani K. Mallick

We derive the tail inequalities between two random variables starting from inequalities between its moment, or more generally between its Lebesgue-Riesz norms, which holds true on certain sets of parameters. We consider some applications…

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

We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…

Methodology · Statistics 2019-03-12 Yuan Ke , Stanislav Minsker , Zhao Ren , Qiang Sun , Wen-Xin Zhou

In this paper, we study moment and concentration inequalities for the spectral norm of sums of dependent random matrices. We establish novel Rosenthal-Burkholder inequalities for discrete-time matrix local martingales,…

Probability · Mathematics 2025-11-13 Yang Peng , Yuchen Xin , Zhihua Zhang

We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…

Statistics Theory · Mathematics 2019-12-23 Hai Shu , Bin Nan

This paper derives exponential tail bounds and polynomial moment inequalities for the spectral norm deviation of a random matrix from its mean value. The argument depends on a matrix extension of Stein's method of exchangeable pairs for…

Probability · Mathematics 2013-05-06 Daniel Paulin , Lester Mackey , Joel A. Tropp

We study the finite-time behaviour of the popular temporal difference (TD) learning algorithm when combined with tail-averaging. We derive finite time bounds on the parameter error of the tail-averaged TD iterate under a step-size choice…

Machine Learning · Computer Science 2024-09-20 Gandharv Patil , Prashanth L. A. , Dheeraj Nagaraj , Doina Precup

We consider a sparse linear regression model with unknown symmetric error under the high-dimensional setting. The true error distribution is assumed to belong to the locally $\beta$-H\"{o}lder class with an exponentially decreasing tail,…

Statistics Theory · Mathematics 2020-09-01 Kyoungjae Lee , Minwoo Chae , Lizhen Lin

We use the theory of Bernstein functions to analyze power law tail behavior with log-periodic perturbations which corresponds to self-similarity of the Bernstein functions. Such tail behavior appears in the context of semistable L\'evy…

Probability · Mathematics 2023-12-22 Peter Kern , Svenja Lage