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Using martingale methods, we obtain some upper bounds for large and moderate deviations of products of independent and identically distributed elements of GL d (R). We investigate all the possible moment conditions, from super-exponential…

Probability · Mathematics 2016-10-25 Christophe Cuny , Jérôme Dedecker , Florence Merlevède

We study the problem of mismatched binary hypothesis testing between i.i.d. distributions. We analyze the tradeoff between the pairwise error probability exponents when the actual distributions generating the observation are different from…

Information Theory · Computer Science 2022-04-28 Parham Boroumand , Albert Guillén i Fàbregas

We study concentration inequalities for the Kullback--Leibler (KL) divergence between the empirical distribution and the true distribution. Applying a recursion technique, we improve over the method of types bound uniformly in all regimes…

Information Theory · Computer Science 2019-10-22 Jay Mardia , Jiantao Jiao , Ervin Tánczos , Robert D. Nowak , Tsachy Weissman

We benchmark the robustness of maximum likelihood based uncertainty estimation methods to outliers in training data for regression tasks. Outliers or noisy labels in training data results in degraded performances as well as incorrect…

Machine Learning · Computer Science 2022-02-09 Deebul S. Nair , Nico Hochgeschwender , Miguel A. Olivares-Mendez

Importance sampling is a popular method for efficient computation of various properties of a distribution such as probabilities, expectations, quantiles etc. The output of an importance sampling algorithm can be represented as a weighted…

Probability · Mathematics 2016-04-18 Henrik Hult , Pierre Nyquist

This paper explores Maximum Likelihood in parametric models in the context of Sanov type Large Deviation Probabilities. MLE in parametric models under weighted sampling is shown to be associated with the minimization of a specific…

Methodology · Statistics 2012-07-30 Michel Broniatowski , Zhansheng Cao

Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have…

Methodology · Statistics 2023-04-07 Matias Salibian-Barrera

In this paper we derive a Large Deviation Principle (LDP) for inhomogeneous U/V-statistics of a general order. Using this, we derive a LDP for two types of statistics: random multilinear forms, and number of monochromatic copies of a…

Probability · Mathematics 2026-04-01 Sohom Bhattacharya , Nabarun Deb , Sumit Mukherjee

Large-deviations theory deals with tails of probability distributions and the rare events of random processes, for example spreading packets of particles. Mathematically, it concerns the exponential fall-of of the density of thin-tailed…

Statistical Mechanics · Physics 2017-07-04 Erez Aghion , David A. Kessler , Eli Barkai

The presence of outlying observations may adversely affect statistical testing procedures that result in unstable test statistics and unreliable inferences depending on the distortion in parameter estimates. In spite of the fact that the…

Methodology · Statistics 2021-04-19 Beste Hamiye Beyaztas , Soutir Bandyopadhyay , Abhijit Mandal

We study the distribution of hard-, soft-, and adaptive soft-thresholding estimators within a linear regression model where the number of parameters k can depend on sample size n and may diverge with n. In addition to the case of known…

Statistics Theory · Mathematics 2012-01-04 Benedikt M. Pötscher , Ulrike Schneider

Mendelian Randomisation (MR) uses genetic variants as instrumental variables to infer causal effects of exposures on an outcome. One key assumption of MR is that the genetic variants used as instrumental variables are independent of the…

Methodology · Statistics 2025-02-21 Maximilian M Mandl , Anne-Laure Boulesteix , Stephen Burgess , Verena Zuber

We consider a longitudinal data structure consisting of baseline covariates, time-varying treatment variables, intermediate time-dependent covariates, and a possibly time dependent outcome. Previous studies have shown that estimating the…

Statistics Theory · Mathematics 2018-10-09 Linh Tran , Maya Petersen , Joshua Schwab , Mark J van der Laan

Outliers widely occur in big-data applications and may severely affect statistical estimation and inference. In this paper, a framework of outlier-resistant estimation is introduced to robustify an arbitrarily given loss function. It has a…

Methodology · Statistics 2023-04-20 Yiyuan She , Zhifeng Wang , Jiahui Shen

In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density estimator, the derivatives estimators exhibit a quadratic…

Statistics Theory · Mathematics 2007-06-13 Abdelkader Mokkadem , Mariane Pelletier , Baba Thiam

We study the out-of-sample properties of robust empirical optimization problems with smooth $\phi$-divergence penalties and smooth concave objective functions, and develop a theory for data-driven calibration of the non-negative "robustness…

Machine Learning · Statistics 2020-05-20 Jun-Ya Gotoh , Michael Jong Kim , Andrew E. B. Lim

In this paper we characterize the possible outliers in the spectrum of large deformed unitarily invariant additive and multiplicative models, as well as the eigenvectors corresponding to them. We allow both the non-deformed unitarily…

Probability · Mathematics 2015-03-23 Serban Teodor Belinschi , Hari Bercovici , Mireille Capitaine , Maxime Fevrier

This paper studies the construction of p-values for nonparametric outlier detection, taking a multiple-testing perspective. The goal is to test whether new independent samples belong to the same distribution as a reference data set or are…

Methodology · Statistics 2024-03-12 Stephen Bates , Emmanuel Candès , Lihua Lei , Yaniv Romano , Matteo Sesia

This paper formulates a penalized empirical likelihood (PEL) method for inference on the population mean when the dimension of the observations may grow faster than the sample size. Asymptotic distributions of the PEL ratio statistic is…

Statistics Theory · Mathematics 2013-02-28 Soumendra N. Lahiri , Subhodeep Mukhopadhyay

Consider the matrix $\Sigma_n = n^{-1/2} X_n D_n^{1/2} + P_n$ where the matrix $X_n \in \C^{N\times n}$ has Gaussian standard independent elements, $D_n$ is a deterministic diagonal nonnegative matrix, and $P_n$ is a deterministic matrix…

Probability · Mathematics 2013-01-23 Francois Chapon , Romain Couillet , Walid Hachem , Xavier Mestre