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We prove two Large deviations principles (LDP) in the zone of moderate deviation probabilities. First we establish LDP for the conditional distributions of moderate deviations of empirical bootstrap measures given empirical probability…

Statistics Theory · Mathematics 2014-05-22 Mikhail Ermakov

Ewens-Pitman model has been successfully applied to various fields including Bayesian statistics. There are four important estimators $K_{n},M_{l,n}$,$K_{m}^{(n)},M_{l,m}^{(n)}$. In particular, $M_{1,n}, M_{1,m}^{(n)}$ are related to…

Probability · Mathematics 2018-11-20 Youzhou Zhou

This paper is devoted to the statistical and numerical properties of the geometric median, and its applications to the problem of robust mean estimation via the median of means principle. Our main theoretical results include (a) an upper…

Statistics Theory · Mathematics 2023-07-21 Stanislav Minsker , Nate Strawn

A moderate deviation principle for functionals, with at most quadratic growth, of moving average processes is established. The main assumptions on the moving average process are a Logarithmic Sobolev inequality for the driving random…

Probability · Mathematics 2007-06-13 Hacene Djellout , Arnaud Guillin , Liming Wu

We examine the problem of construction of confidence intervals within the basic single-parameter, single-iteration variation of the method of quasi-optimal weights. Two kinds of distortions of such intervals due to insufficiently large…

Data Analysis, Statistics and Probability · Physics 2020-05-27 A. D. Morozov , A. V. Lokhov , F. V. Tkachov

Motivated by the study of dependent random variables by coupling with independent blocks of variables, we obtain first sufficient conditions for the moderate deviation principle in its functional form for triangular arrays of independent…

Probability · Mathematics 2008-05-07 Florence Merlevede , Magda Peligrad

We consider the problem of constructing confidence intervals for the median of a response $Y \in \mathbb{R}$ conditional on features $X \in \mathbb{R}^d$ in a situation where we are not willing to make any assumption whatsoever on the…

Statistics Theory · Mathematics 2021-09-07 Dhruv Medarametla , Emmanuel J. Candès

Researchers increasingly use meta-analysis to synthesize the results of several studies in order to estimate a common effect. When the outcome variable is continuous, standard meta-analytic approaches assume that the primary studies report…

The goal of this note is to present a modification of the popular median of means estimator that achieves sub-Gaussian deviation bounds with nearly optimal constants under minimal assumptions on the underlying distribution. We build on a…

Statistics Theory · Mathematics 2023-05-31 Stanislav Minsker

We define two minimum distance estimators for dependent data by minimizing some approximated Maximum Mean Discrepancy distances between the true empirical distribution of observations and their assumed (parametric) model distribution. When…

Methodology · Statistics 2026-01-19 Pierre Alquier , Jean-David Fermanian , Benjamin Poignard

For the zone of moderate deviation probabilities the local asymptotic minimax lower bound of asymptotic efficiency of estimators is established. The estimation parameter is multidimensional. The lower bound admits the interpretation as the…

Statistics Theory · Mathematics 2012-06-08 Mikhail Ermakov

A moderate deviation principle for nonlinear functions of Gaussian processes is established. The nonlinear functions need not be locally bounded. Especially, the logarithm is allowed. (Thus, small deviations of the process are relevant.)…

Probability · Mathematics 2007-05-23 Boris Tsirelson

Cram\'er's moderate deviations give a quantitative estimate for the relative error of the normal approximation and provide theoretical justifications for many estimator used in statistics. In this paper, we establish self-normalized…

Probability · Mathematics 2025-03-03 Xiequan Fan , Qi-Man Shao

The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and scantily understood for random fields. Here it is established for splittable random…

Probability · Mathematics 2018-10-16 Boris Tsirelson

We present deviation bounds for self-normalized averages and applications to estimation with a random number of observations. The results rely on a peeling argument in exponential martingale techniques that represents an alternative to the…

Statistics Theory · Mathematics 2016-11-17 Aurélien Garivier

We consider the problem of interval estimation of the odds ratio. An asymptotic confidence interval is widely applied in medical research. Unfortunately that confidence interval has a poor coverage probability: it is significantly smaller…

Methodology · Statistics 2020-11-19 Zofia Zielińska-Kolasińska , Wojciech Zieliński

This is basically a polished presentation for Sections 1,2 of arXiv:0801.1050. The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and…

Probability · Mathematics 2016-12-28 Boris Tsirelson

In this paper we consider the (weighted) spectral measure $\mu_n$ of a $n\times n$ random matrix, distributed according to a classical Gaussian, Laguerre or Jacobi ensemble, and show a moderate deviation principle for the standardised…

Probability · Mathematics 2013-08-27 Jan Nagel

Suppose data are fitted to some parametric model but that the true model happens to be one with an additional parameter. When a parameter is to be estimated one can use likelihood estimation in the wider model or in the narrow model.…

Methodology · Statistics 2026-03-27 Nils Lid Hjort

We establish Cram\'er-type moderate deviation theorems for sums of locally dependent random variables and combinatorial central limit theorems. Under some mild exponential moment conditions, optimal error bounds and convergence ranges are…

Probability · Mathematics 2021-12-22 Song-Hao Liu , Zhuo-Song Zhang