Related papers: Deviation inequalities and moderate deviations for…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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.
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…