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Sample average approximation (SAA), a popular method for tractably solving stochastic optimization problems, enjoys strong asymptotic performance guarantees in settings with independent training samples. However, these guarantees are not…

Optimization and Control · Mathematics 2021-12-13 Yafei Wang , Bo Pan , Wei Tu , Peng Liu , Bei Jiang , Chao Gao , Wei Lu , Shangling Jui , Linglong Kong

The paper compares probabilistic and exact methods for estimating the asymptotic behavior of summation arithmetic functions, and estimates of the results are obtained by precise methods. Conditions for stationarity in the broad sense are…

Number Theory · Mathematics 2018-06-11 Victor Volfson

Strongly consistent and asymptotically normal estimators of the Hurst parameter of solutions of stochastic differential equations are proposed. The estimators are based on discrete observations of the underlying processes.

Probability · Mathematics 2015-07-28 Kestutis Kubilius , Viktor Skorniakov

We consider stochastic versions of the Cauchy exponential functional equation and give a martingale characterization of the general solution.

Probability · Mathematics 2021-12-30 Beso Chikvinidze , Michael Mania , Revaz Tevzadze

The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…

Statistics Theory · Mathematics 2022-08-04 Taras Bodnar , Dmitry Otryakhin , Erik Thorsen

We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical…

Statistics Theory · Mathematics 2012-02-24 Peter Hall , Tung Pham , M. P. Wand , S. S. J. Wang

Stochastic symmetries and related invariance properties of finite dimensional SDEs driven by general c\`adl\`ag semimartingales taking values in Lie groups are defined and investigated. In order to enlarge the class of possible symmetries…

Probability · Mathematics 2017-08-08 Sergio Albeverio , Francesco C. De Vecchi , Paola Morando , Stefania Ugolini

The paper studies asymptotic properties of estimators of multidimensional stochastic differential equations driven by Brownian motions from high-frequency discrete data. Consistency and central limit properties of a class of estimators of…

Statistics Theory · Mathematics 2024-11-07 Arnab Ganguly

In this paper we propose and study a general class of Gaussian Semiparametric Estimators (GSE) of the fractional differencing parameter in the context of long-range dependent multivariate time series. We establish large sample properties of…

Statistics Theory · Mathematics 2022-11-16 Guilherme Pumi , Sílvia R. C. Lopes

Consider $n$ i.i.d. random elements on $C[0,1]$. We show that, under an appropriate strengthening of the domain of attraction condition, natural estimators of the extreme-value index, which is now a continuous function, and the normalizing…

Statistics Theory · Mathematics 2007-06-13 John H. J. Einmahl , Tao Lin

Delattre et al. (2013) considered n independent stochastic differential equations (SDEs), where in each case the drift term is associated with a random effect, the distribution of which depends upon unknown parameters. Assuming the…

Statistics Theory · Mathematics 2016-05-12 Trisha Maitra , Sourabh Bhattacharya

We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a non-asymptotic point of view. In particular, we define estimators with a…

Statistics Theory · Mathematics 2015-09-22 Luc Devroye , Matthieu Lerasle , Gabor Lugosi , Roberto I. Oliveira

We present results on parameter estimation and non-parameter estimation of the linear partially observed Gaussian system of stochastic differential equations. We propose new one-step estimators which have the same asymptotic properties as…

Statistics Theory · Mathematics 2019-04-23 Yury A. Kutoyants , Li Zhou

We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…

Statistics Theory · Mathematics 2020-01-22 Jean-Marc Azaïs , François Bachoc , Agnès Lagnoux , Thi Mong Ngoc Nguyen

We develop a new generalized coupling approach to the study of stochastic delay equations with H\"older continuous coefficients, for which analytical PDE-based methods are not available. We prove that such equations possess unique weak…

Probability · Mathematics 2018-08-21 Alexei Kulik , Michael Scheutzow

We study the problem of estimating the covariance parameters of a one-dimensional Gaussian process with exponential covariance function under fixed-domain asymptotics. We show that the weighted pairwise maximum likelihood estimator of the…

Statistics Theory · Mathematics 2019-07-15 François Bachoc , Moreno Bevilacqua , Daira Velandia

In the estimation of the mean matrix in a multivariate normal distribution, the generalized Bayes estimators with closed forms are provided, and the sufficient conditions for their minimaxity are derived relative to both matrix and scalar…

Statistics Theory · Mathematics 2021-08-16 Ryota Yuasa , Tatsuya Kubokawa

This article provides an introduction to the asymptotic analysis of covariance parameter estimation for Gaussian processes. Maximum likelihood estimation is considered. The aim of this introduction is to be accessible to a wide audience and…

Statistics Theory · Mathematics 2020-09-16 François Bachoc

General stochastic Euler schemes for ordinary differential equations are studied. We give proofs on the consistency, the rate of convergence and the asymptotic normality of these procedures.

Probability · Mathematics 2017-02-09 Johannes T. N. Krebs

General depth weighted scatter estimators are introduced and investigated. For general depth functions, we find out that these affine equivariant scatter estimators are Fisher consistent and unbiased for a wide range of multivariate…

Statistics Theory · Mathematics 2007-06-13 Yijun Zuo , Hengjian Cui