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This paper deals with Poisson approximation to weighted sums of locally dependent random variables using Stein's method. The derived result represents a significant improvement of existing results. To illustrate the effectiveness of our…

Probability · Mathematics 2023-12-08 Pratima Eknath Kadu

Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…

Methodology · Statistics 2018-04-10 German A. Schnaidt Grez , Brani Vidakovic

We study the nonparametric estimation of the jump density of a compound Poisson process from the discrete observation of one trajectory over $[0,T]$. We consider the microscopic regime when the sampling rate $\Delta=\Delta_T\rightarrow0$ as…

Statistics Theory · Mathematics 2012-03-15 Céline Duval

It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for…

Classical Analysis and ODEs · Mathematics 2010-04-28 Thomas Hangelbroek , Amos Ron

Rue and Held (2005) proposed a method for efficiently computing the Gaussian likelihood for stationary Markov random field models, when the data locations fall on a complete regular grid, and the model has no additive error term. The…

Computation · Statistics 2019-12-16 Joseph Guinness , Ilse C. F. Ipsen

A Stiefel manifold of the compact type is often encountered in many fields of Engineering including, signal and image processing, machine learning, numerical optimization and others. The Stiefel manifold is a Riemannian homogeneous space…

Computer Vision and Pattern Recognition · Computer Science 2017-08-02 Rudrasis Chakraborty , Baba Vemuri

Using a semi-parametric approach based on the fourth-order Edgeworth expansion for the unknown signal distribution, we derive an explicit expression for the likelihood detection statistic in the presence of non-normally distributed…

Cosmology and Nongalactic Astrophysics · Physics 2015-06-19 Lionel Martellini , Tania Regimbau

We consider nonparametric statistical inference on a periodic interaction potential $W$ from noisy discrete space-time measurements of solutions $\rho=\rho_W$ of the nonlinear McKean-Vlasov equation, describing the probability density of…

Statistics Theory · Mathematics 2025-01-15 Richard Nickl , Grigorios A. Pavliotis , Kolyan Ray

The velocity of a passive particle in a one-dimensional wave field is shown to converge in law to a Wiener process, in the limit of a dense wave spectrum with independent complex amplitudes, where the random phases distribution is invariant…

Mathematical Physics · Physics 2012-07-12 Yves Elskens

We derive Gaussian approximation bounds for $k$-Potential Nearest Neighbor ($k$-PNN) based random forest predictions based on a set of training points given by a Poisson process under fairly mild regularity assumptions on the data…

Statistics Theory · Mathematics 2025-05-06 Zhaoyang Shi , Chinmoy Bhattacharjee , Krishnakumar Balasubramanian , Wolfgang Polonik

Parametric density estimation, for example as Gaussian distribution, is the base of the field of statistics. Machine learning requires inexpensive estimation of much more complex densities, and the basic approach is relatively costly…

Machine Learning · Computer Science 2017-02-21 Jarek Duda

In 2018, Bourgain pioneered a novel perturbative harmonic-analytic approach to the stochastic homogenization theory of discrete elliptic equations with weakly random i.i.d. coefficients. The approach was subsequently refined to show that…

Analysis of PDEs · Mathematics 2024-06-17 Mitia Duerinckx , Marius Lemm , François Pagano

The aim of this research is to examine various statistical approximation properties with respect to Kantorovich \textit{\text{\texthtq}}-Baskakov operators using wavelets. We discuss and investigate a weighted statistical approximation…

General Mathematics · Mathematics 2023-05-18 Mohammad Ayman-Mursaleen , Bishnu P. Lamichhane , Adem Kiliçman , Norazak Senu

Random fields on the sphere play a fundamental role in the natural sciences. This paper presents a simulation algorithm parenthetical to the spectral turning bands method used in Euclidean spaces, for simulating scalar- or vector-valued…

Statistics Theory · Mathematics 2020-03-31 Alfredo Alegría , Xavier Emery , Christian Lantuéjoul

Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…

Statistics Theory · Mathematics 2025-04-02 Guoyu Zhang , Dandan Jiang , Fang Yao

We compare different nonlinear approximations to gravitational clustering in the weakly nonlinear regime, using as a comparative statistic the evolution of non-Gaussianity which can be characterised by a set of numbers $S_p$ describing…

Astrophysics · Physics 2009-10-22 Dipak Munshi , Varun Sahni , Alexei A. Starobinsky

A popular approach for modeling and inference in spatial statistics is to represent Gaussian random fields as solutions to stochastic partial differential equations (SPDEs) of the form $L^{\beta}u = \mathcal{W}$, where $\mathcal{W}$ is…

Methodology · Statistics 2019-12-03 David Bolin , Kristin Kirchner

We study non-parametric regression estimates for random fields. The data satisfies certain strong mixing conditions and is defined on the regular $N$-dimensional lattice structure. We show consistency and obtain rates of convergence. The…

Statistics Theory · Mathematics 2018-07-06 Johannes T. N. Krebs

Working with a toy model whose partition function consists of a discrete summation, we introduce the statistical field-theory methodology by transforming a partition function via a formal Gaussian integral relation (the Hubbard-Stratonovich…

Statistical Mechanics · Physics 2016-09-05 Derek Frydel

We propose a projection-based class of uniformity tests on the hypersphere using statistics that integrate, along all possible directions, the weighted quadratic discrepancy between the empirical cumulative distribution function of the…