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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

A large deviation principle is derived for stochastic partial differential equations with slow-fast components. The result shows that the rate function is exactly that of the averaged equation plus the fluctuating deviation which is a…

Probability · Mathematics 2010-01-28 Wei Wang , A. J. Roberts , Jinqiao Duan

This paper is the second part of our study on the non-parametric estimation of MS-NAR processes started with [L. Fermin et al. 2017]. We consider the Nadaraya-Watson type regression function estimator for non-linear autoregressive Markov…

Methodology · Statistics 2026-04-01 Lisandro Fermin , Ricardo Rios , Luis-Ángel Rodríguez

For solving pseudo-convex global optimization problems, we present a novel fully adaptive steepest descent method (or ASDM) without any hard-to-estimate parameters. For the step-size regulation in an $\varepsilon$-normalized direction, we…

Optimization and Control · Mathematics 2021-08-12 Z. R. Gabidullina

This paper is a study on solutions of the Sample Average Approximation Method to solve compound stochastic programs. We derive nonasymptotic upper estimates for probabilities of the approximation errors. The results depend on the sample…

Optimization and Control · Mathematics 2025-08-29 Volker Kratschmer

This study introduces a debiasing method for regression estimators, including high-dimensional and nonparametric regression estimators. For example, nonparametric regression methods allow for the estimation of regression functions in a…

Machine Learning · Statistics 2024-11-27 Masahiro Kato

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

Motivated by learning of correlated equilibria in non-cooperative games, we perform a large deviations analysis of a regret minimizing stochastic approximation algorithm. The regret minimization algorithm we consider comprises multiple…

Optimization and Control · Mathematics 2024-06-04 Hongjiang Qian , Vikram Krishnamurthy

Stochastic gradient methods are among the most widely used algorithms for large-scale optimization and machine learning. A key technique for improving the statistical efficiency and stability of these methods is the use of averaging schemes…

Optimization and Control · Mathematics 2026-03-11 K. Lakshmanan

We establish the large deviations principle (LDP) and the moderate deviations principle (MDP) and an almost sure version of the central limit theorem (CLT) for the stochastic 3D viscous primitive equations driven by a multiplicative white…

Probability · Mathematics 2020-10-27 Jakub Slavík

The density weighted average derivative (DWAD) of a regression function is a canonical parameter of interest in economics. Classical first-order large sample distribution theory for kernel-based DWAD estimators relies on tuning parameter…

Econometrics · Economics 2024-02-16 Matias D. Cattaneo , Max H. Farrell , Michael Jansson , Ricardo Masini

Non linear regression models are a standard tool for modeling real phenomena, with several applications in machine learning, ecology, econometry... Estimating the parameters of the model has garnered a lot of attention during many years. We…

Statistics Theory · Mathematics 2020-09-17 Peggy Cénac , Antoine Godichon-Baggioni , Bruno Portier

Many machine learning applications and tasks rely on the stochastic gradient descent (SGD) algorithm and its variants. Effective step length selection is crucial for the success of these algorithms, which has motivated the development of…

Machine Learning · Computer Science 2023-05-18 Shigeng Sun , Yuchen Xie

This work explores the use of a forward-backward martingale method together with a decoupling argument and entropic estimates between the conditional and averaged measures to prove a strong averaging principle for stochastic differential…

Probability · Mathematics 2017-09-18 Bob Pepin

In this work we study the averaging principle for non-autonomous slow-fast systems of stochastic differential equations. In particular in the first part we prove the averaging principle assuming the sublinearity, the Lipschitzianity and the…

Probability · Mathematics 2021-01-12 Filippo de Feo

In this work, we investigate stochastic quasi-Newton methods for minimizing a finite sum of cost functions over a decentralized network. In Part I, we develop a general algorithmic framework that incorporates stochastic quasi-Newton…

Optimization and Control · Mathematics 2023-03-22 Jiaojiao Zhang , Huikang Liu , Anthony Man-Cho So , Qing Ling

We study constrained nested stochastic optimization problems in which the objective function is a composition of two smooth functions whose exact values and derivatives are not available. We propose a single time-scale stochastic…

Optimization and Control · Mathematics 2019-09-09 Saeed Ghadimi , Andrzej Ruszczyński , Mengdi Wang

In this paper, we consider McKean-Vlasov stochastic differential equations (MVSDEs) driven by L\'evy noise. By identifying the right equations satisfied by the solutions of the MVSDEs with shifted driving L\'evy noise, we build up a…

Probability · Mathematics 2020-11-18 Wei Liu , Yulin Song , Jianliang Zhai , Tusheng Zhang

We present a novel statistical inference framework for convex empirical risk minimization, using approximate stochastic Newton steps. The proposed algorithm is based on the notion of finite differences and allows the approximation of a…

Machine Learning · Computer Science 2019-02-06 Tianyang Li , Anastasios Kyrillidis , Liu Liu , Constantine Caramanis

In this paper, we study large and moderate deviation principles for stochastic partial differential equations (SPDEs) on metric graphs and their associated multiscale models via the weak convergence approach, providing a refined…

Probability · Mathematics 2025-09-09 Jianbo Cui , Derui Sheng