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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 multivariate errors-in-variables regression model is applicable when both dependent and independent variables in a multivariate regression are subject to measurement errors. In such a scenario it is long established that the traditional…

Statistics Theory · Mathematics 2015-10-14 Johannes Lutzeyer , Edward A. K. Cohen

In this paper we obtain a Bernstein type inequality for a class of weakly dependent and bounded random variables. The proofs lead to a moderate deviations principle for sums of bounded random variables with exponential decay of the strong…

Probability · Mathematics 2012-02-23 Florence Merlevède , Magda Peligrad , Emmanuel Rio

We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…

Methodology · Statistics 2019-09-09 Alexandre Belloni , Abhishek Kaul , Mathieu Rosenbaum

Inverse optimization has been increasingly used to estimate unknown parameters in an optimization model based on decision data. We show that such a point estimation is insufficient in a prescriptive setting where the estimated parameters…

Optimization and Control · Mathematics 2025-02-11 Bo Lin , Erick Delage , Timothy C. Y. Chan

We study adaptive estimation and inference in ill-posed linear inverse problems defined by conditional moment restrictions. Existing regularized estimators such as Regularized DeepIV (RDIV) require prior knowledge of the smoothness of the…

Machine Learning · Statistics 2026-03-03 Jiyuan Tan , Vasilis Syrgkanis

The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…

Econometrics · Economics 2024-02-27 Felix Chan , Laszlo Matyas

In this paper, a modification of the conventional approximations to the quasi-maximum likelihood method is introduced for the parameter estimation of diffusion processes from discrete observations. This is based on a convergent…

Optimization and Control · Mathematics 2013-12-19 J. C. Jimenez

By using the weak convergence method, we establish the large and moderate deviation principles for the multivalued McKean-Vlasov SDEs with non-Lipschitz coefficients driven by L\'{e}vy noise in this paper. The Bihari's inequality is used to…

Probability · Mathematics 2025-12-25 Lingyan Cheng , Caihong Gu , Wei Liu , Fengwu Zhu

In this paper, we establish a central limit theorem and a moderate deviations for 2D stochastic primitive equations with multiplicative noise. The proof is mainly based on the weak convergence approach.

Probability · Mathematics 2017-07-10 Rangrang Zhang , Guoli Zhou

A nearly unstable sequence of stationary spatial autoregressive processes is investigated, when the sum of the absolute values of the autoregressive coefficients tends to one. It is shown that after an appropriate norming the least squares…

Statistics Theory · Mathematics 2008-03-18 Sándor Baran , Gyula Pap

We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…

Computer Vision and Pattern Recognition · Computer Science 2021-03-12 Takumi Kawashima , Qing Yu , Akari Asai , Daiki Ikami , Kiyoharu Aizawa

In this paper, we establish a moderate deviation principle for stochastic models of two-dimensional second grade fluids driven by L\'evy noise. We will adopt the weak convergence approach. Because of the appearance of jumps, this result is…

Probability · Mathematics 2018-01-26 Wuting Zheng , Jianliang Zhai , Tusheng Zhang

We provide a unifying treatment of pathwise moderate deviations for models commonly used in financial applications, and for related integrated functionals. Suitable scaling allows us to transfer these results into small-time, large-time and…

Mathematical Finance · Quantitative Finance 2018-12-04 Antoine Jacquier , Konstantinos Spiliopoulos

We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced…

Probability · Mathematics 2017-11-28 Andrew Papanicolaou , Konstantinos Spiliopoulos

The main object of investigation in this paper is a very general regression model in optional setting - when an observed process is an optional semimartingale depending on an unknown parameter. It is well-known that statistical data may…

Statistics Theory · Mathematics 2021-03-16 Mohamed Abdelghani , Alexander Melnikov , Andrey Pak

Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is…

Numerical Analysis · Mathematics 2015-06-05 Aleksandr Y. Aravkin , Tristan van Leeuwen

In various statistical settings, the goal is to estimate a function which is restricted by the statistical model only through a conditional moment restriction. Prominent examples include the nonparametric instrumental variable framework for…

Methodology · Statistics 2025-05-28 AmirEmad Ghassami , James M. Robins , Andrea Rotnitzky

Partial differential equation parameter estimation is a mathematical and computational process used to estimate the unknown parameters in a partial differential equation model from observational data. This paper employs a greedy sampling…

Dynamical Systems · Mathematics 2024-05-15 Ali Forootani , Harshit Kapadia , Sridhar Chellappa , Pawan Goyal , Peter Benner

We derive moderate deviation principles for the trajectory of the empirical magnetization of the standard Curie-Weiss model via a general analytic approach based on convergence of generators and uniqueness of viscosity solutions for…

Probability · Mathematics 2017-10-13 Francesca Collet , Richard Kraaij