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Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…

Optimization and Control · Mathematics 2018-05-22 Mark Cannon

This paper is devoted to establishing exponential bounds for the probabilities of deviation of a sample sum from its expectation, when the variables involved in the summation are obtained by sampling in a finite population according to a…

Statistics Theory · Mathematics 2016-10-13 Patrice Bertail , Stephan Clémençon

We consider the asymptotics of various estimators based on a large sample of branching trees from a critical multi-type Galton-Watson process, as the sample size increases to infinity. The asymptotics of additive functions of trees, such as…

Probability · Mathematics 2007-05-23 Zhiyi Chi

We consider learning methods based on the regularization of a convex empirical risk by a squared Hilbertian norm, a setting that includes linear predictors and non-linear predictors through positive-definite kernels. In order to go beyond…

Machine Learning · Computer Science 2019-06-19 Ulysse Marteau-Ferey , Dmitrii Ostrovskii , Francis Bach , Alessandro Rudi

We present the first minimax risk bounds for estimators of the spectral measure in multivariate linear factor models, where observations are linear combinations of regularly varying latent factors. Non-asymptotic convergence rates are…

Statistics Theory · Mathematics 2024-11-12 Xuhui Zhang , Jose Blanchet , Youssef Marzouk , Viet Anh Nguyen , Sven Wang

For $V : \mathbb{R}^d \to \mathbb{R}$ coercive, we study the convergence rate for the $L^1$-distance of the empiric minimizer, which is the true minimum of the function $V$ sampled with noise with a finite number $n$ of samples, to the…

Statistics Theory · Mathematics 2023-03-09 Pierre Bras

We derive a posteriori error estimators for an optimal control problem governed by a convection-reaction-diffusion equation; control constraints are also considered. We consider a family of low-order stabilized finite element methods to…

Numerical Analysis · Mathematics 2017-04-24 Alejandro Allendes , Enrique Otarola , Richard Rankin

A general asymptotic theory is given for the panel data AR(1) model with time series independent in different cross sections. The theory covers the cases of stationary process, nearly non-stationary process, unit root process, mildly…

Applications · Statistics 2016-11-15 Jianfei Shen , Tianxiao Pang

In this paper we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the…

Probability · Mathematics 2017-12-05 Denis Belomestny , Stefan Häfner , Mikhail Urusov

In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…

Machine Learning · Statistics 2022-06-08 Michał Dereziński , Manfred K. Warmuth , Daniel Hsu

Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…

Statistics Theory · Mathematics 2020-12-15 Sheng Jiang , Surya T. Tokdar

A weighted regression procedure is proposed for regression type problems where the innovations are heavy-tailed. This method approximates the least absolute regression method in large samples, and the main advantage will be if the sample is…

Computation · Statistics 2018-11-06 J. Martin van Zyl

In this paper, the estimation of parameters in the harmonic regression with cyclically dependent errors is addressed. Asymptotic properties of the least-squares estimates are analyzed by simulation experiments. By numerical simulation, we…

We consider the problem of approximating an unknown function $u\in L^2(D,\rho)$ from its evaluations at given sampling points $x^1,\dots,x^n\in D$, where $D\subset \mathbb{R}^d$ is a general domain and $\rho$ is a probability measure. The…

Numerical Analysis · Mathematics 2018-05-29 Benjamin Arras , Markus Bachmayr , Albert Cohen

We consider the problem of estimating the slope parameter in circular functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of 1-periodic, second order stationary random functions X1,...,Xn. We consider an…

Statistics Theory · Mathematics 2010-10-01 Fabienne Comte , Jan Johannes

In recent papers it has been demonstrated that sampling a Gibbs distribution from an appropriate time-irreversible Langevin process is, from several points of view, advantageous when compared to sampling from a time-reversible one. Adding…

Probability · Mathematics 2015-02-20 Luc Rey-Bellet , Konstantinos Spiliopoulos

Importance sampling is a popular variance reduction method for Monte Carlo estimation, where a notorious question is how to design good proposal distributions. While in most cases optimal (zero-variance) estimators are theoretically…

Statistics Theory · Mathematics 2021-02-22 Carsten Hartmann , Lorenz Richter

The problem of the estimation of relevance to a set of histograms generated by samples of a discrete time process is discussed on the base of the variational principles proposed in the previous paper [1]. Some conditions for dimension…

Optimization and Control · Mathematics 2018-05-28 M. A. Antonets

This paper is devoted to the problem of determining the concentration bounds that are achievable in non-parametric regression. We consider the setting where features are supported on a bounded subset of $\mathbb{R}^d$, the regression…

Statistics Theory · Mathematics 2024-12-02 Anna Ben-Hamou , Arnaud Guyader

We define and analyse a least-squares finite element method for a first-order reformulation of a scaled Brinkman model of fluid flow through porous media. We introduce a pseudostress variable that allows to eliminate the pressure variable…

Numerical Analysis · Mathematics 2022-11-17 Thomas Führer , Juha Videman