English
Related papers

Related papers: Moderate deviation principle for the chi-square st…

200 papers

This work studies a two-time-scale functional system given by two jump-diffusions under the scale separation by a small parameter $\varepsilon \rightarrow 0$. The coefficients of the equations that govern the dynamics of the system depend…

Probability · Mathematics 2022-07-15 André de Oliveira Gomes , Pedro Catuogno

This paper regards randomized discrete-time consensus systems that preserve the average "on average". As a main result, we provide an upper bound on the mean square deviation of the consensus value from the initial average. Then, we apply…

Optimization and Control · Mathematics 2013-04-19 Paolo Frasca , Julien M. Hendrickx

By comparing the original equations with the corresponding stationary ones, the moderate deviation principle (MDP) is established for unbounded additive functionals of several different models of distribution dependent SDEs, with…

Probability · Mathematics 2021-01-26 Panpan Ren , Shen Wang

We show that for local alternatives to uniformity which are determined by a sequence of square integrable densities the moderate deviation (MD) theorem for the corresponding Neyman-Pearson statistic does not hold in the full range for all…

Statistics Theory · Mathematics 2020-03-27 Tadeusz Inglot

A moderate deviations principle for the law of a stochastic Burgers equation is proved via the weak convergence approach. In addition, some useful estimates toward a central limit theorem are established.

Probability · Mathematics 2020-01-17 Rachid Belfadli , Lahcen Boulanba , Mohamed Mellouk

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

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 some planary random…

Probability · Mathematics 2019-09-25 Boris Tsirelson

It is well-known that each statistic in the family of power divergence statistics, across $n$ trials and $r$ classifications with index parameter $\lambda\in\mathbb{R}$ (the Pearson, likelihood ratio and Freeman-Tukey statistics correspond…

Statistics Theory · Mathematics 2021-12-28 Robert E. Gaunt

In the present paper, we consider the moderate deviation principle for the plug-in estimators of a large class of diversity indices on countable alphabets, where the distribution may change with the sample size. Our results cover some of…

Statistics Theory · Mathematics 2025-08-19 Zhenhong Yu , Yu Miao

We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.

Probability · Mathematics 2007-07-11 Fabrice Gamboa , Thierry Klein , Clémentine Prieur

Moderate deviation principle is achieved by the weak convergence approach for a stochastic Schr\"odinger type equation with linear drift term and noise driven by a $Q$-Wiener process. The central limit theorem is also shown for the equation…

Probability · Mathematics 2024-09-27 Parisa Fatheddin , Hannelore Lisei

Consider the state space model (X_t,Y_t), where (X_t) is a Markov chain, and (Y_t) are the observations. In order to solve the so-called filtering problem, one has to compute L(X_t|Y_1,...,Y_t), the law of X_t given the observations…

Probability · Mathematics 2007-05-23 R. Douc , A. Guillin , J. Najim

In this paper, we consider the normalized least squares estimator of the parameter in a mildly stationary first-order autoregressive (AR(1)) model with dependent errors which are modeled as a mildly stationary AR(1) process. By martingale…

Probability · Mathematics 2023-11-08 Hui Jiang , Guangyu Yang , Mingming Yu

We prove a moderate deviations principles for the size of the largest connected component in a random $d$-uniform hypergraph. The key tool is a version of the exploration process, that is also used to investigate the giant component of an…

Probability · Mathematics 2019-07-19 Jingjia Liu , Matthias Löwe

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

This paper concerns the development of Stein's method for chi-square approximation and its application to problems in statistics. New bounds for the derivatives of the solution of the gamma Stein equation are obtained. These bounds involve…

Probability · Mathematics 2017-05-30 Robert E. Gaunt , Alastair Pickett , Gesine Reinert

The two-parameter Poisson-Dirichlet distribution is the law of a sequence of decreasing nonnegative random variables with total sum one. It can be constructed from stable and Gamma subordinators with the two-parameters, $\alpha$ and…

Probability · Mathematics 2009-06-15 Shui Feng , Fuqing Gao

We consider a stable but nearly unstable autoregressive process of any order. The bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with spectral radius $\rho(A_{n}) < 1$ satisfying…

Statistics Theory · Mathematics 2019-10-17 Frédéric Proïa

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 propose the use of a simple intuitive principle for measuring algorithmic classification bias: the significance of the differences in a classifier's error rates across the various demographics is inversely commensurate with the sample…

Methodology · Statistics 2026-01-08 Ioannis Ivrissimtzis , Shauna Concannon , Matthew Houliston , Graham Roberts