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Asymptotic equivalence in Le Cam's sense for nonparametric regression experiments is extended to the case of non-regular error densities, which have jump discontinuities at their endpoints. We prove asymptotic equivalence of such regression…

Statistics Theory · Mathematics 2011-01-28 Alexander Meister , Markus Reiß

A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…

Methodology · Statistics 2019-07-25 Shinichiro Shirota , Andrew O. Finley , Bruce D. Cook , Sudipto Banerjee

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

Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…

Machine Learning · Statistics 2015-11-25 Leo L. Duan , Xia Wang , Rhonda D. Szczesniak

We study estimation and prediction of Gaussian processes with covariance model belonging to the generalized Cauchy (GC) family, under fixed domain asymptotics. Gaussian processes with this kind of covariance function provide separate…

Methodology · Statistics 2019-07-23 Moreno Bevilacqua , Tarik Faouzi

The aim of this paper is to present an extension of the well-known as-ymptotic equivalence between density estimation experiments and a Gaussian white noise model. Our extension consists in enlarging the nonparametric class of the…

Probability · Mathematics 2015-03-18 Ester Mariucci

We study estimation and prediction of Gaussian random fields with covariance models belonging to the generalized Wendland (GW) class, under fixed domain asymptotics. As the Mat\'ern case, this class allows a continuous parameterization of…

Statistics Theory · Mathematics 2017-11-17 M. Bevilacqua , T. Faouzi , R. Furrer , E. Porcu

A spatial point process can be characterized by an intensity function which predicts the number of events that occur across space. In this paper, we develop a method to infer predictive intensity intervals by learning a spatial model using…

Machine Learning · Statistics 2020-07-06 Muhammad Osama , Dave Zachariah , Petre Stoica

We consider the statistical experiment given by a sample of a stationary Gaussian process with an unknown smooth spectral density f. Asymptotic equivalence, in the sense of Le Cam's deficiency Delta-distance, to two Gaussian experiments…

Statistics Theory · Mathematics 2009-03-10 Georgi K. Golubev , Michael Nussbaum , Harrison H. Zhou

We consider a general class of statistical experiments, in which an $n$-dimensional centered Gaussian random variable is observed and its covariance matrix is the parameter of interest. The covariance matrix is assumed to be…

Statistics Theory · Mathematics 2025-01-17 Cristina Butucea , Alexander Meister , Angelika Rohde

interpretable, and well understood models that are routinely employed even though, as is revealed through prior and posterior predictive checks, these can poorly characterise the spatial heterogeneity in the underlying process of interest.…

Machine Learning · Statistics 2024-04-08 Andrew Zammit-Mangion , Michael D. Kaminski , Ba-Hien Tran , Maurizio Filippone , Noel Cressie

When modelling time series, it is common to decompose observed variation into a "signal" process, the process of interest, and "noise", representing nuisance factors that obfuscate the signal. To separate signal from noise, assumptions must…

Methodology · Statistics 2020-11-11 Richard Creswell , Ben Lambert , Chon Lok Lei , Martin Robinson , David Gavaghan

With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model…

Methodology · Statistics 2019-10-24 Pulong Ma , Emily L. Kang

We prove asymptotic equivalence of nonparametric additive regression and an appropriate Gaussian white noise experiment in which a multidimensional shifted Wiener process is observed, whose dimension equals the number of additive…

Statistics Theory · Mathematics 2026-02-12 Moritz Jirak , Alexander Meister , Angelika Rohde

A problem of current interest is the estimation of spatially distributed processes at locations where measurements are missing. Linear interpolation methods rely on the Gaussian assumption, which is often unrealistic in practice, or…

Data Analysis, Statistics and Probability · Physics 2013-01-09 Milan Žukovič , Dionissios T. Hristopulos

We present a probabilistic model where the latent variable respects both the distances and the topology of the modeled data. The model leverages the Riemannian geometry of the generated manifold to endow the latent space with a well-defined…

Machine Learning · Statistics 2021-06-09 Martin Jørgensen , Søren Hauberg

Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of…

Machine Learning · Computer Science 2026-04-08 Matteo Bosso , Giovanni Franzese , Kushal Swamy , Maarten Theulings , Alejandro M. Aragón , Farbod Alijani

We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to lead to an…

Statistics Theory · Mathematics 2015-03-19 Markus Bibinger , Markus Reiß

We consider covariance parameter estimation for a Gaussian process under inequality constraints (boundedness, monotonicity or convexity) in fixed-domain asymptotics. We address the estimation of the variance parameter and the estimation of…

Statistics Theory · Mathematics 2021-11-04 François Bachoc , Agnès Lagnoux , Andrés F. López-Lopera

Estimating associations between spatial covariates and responses - rather than merely predicting responses - is central to environmental science, epidemiology, and economics. For instance, public health officials might be interested in…

Machine Learning · Statistics 2025-11-11 David R. Burt , Renato Berlinghieri , Stephen Bates , Tamara Broderick