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This paper develops a general asymptotic theory of local polynomial (LP) regression for spatial data observed at irregularly spaced locations in a sampling region $R_n \subset \mathbb{R}^d$. We adopt a stochastic sampling design that can…

Statistics Theory · Mathematics 2023-12-27 Daisuke Kurisu , Yasumasa Matsuda

Recent advances in machine learning have been achieved by using overparametrized models trained until near interpolation of the training data. It was shown, e.g., through the double descent phenomenon, that the number of parameters is a…

Machine Learning · Statistics 2024-03-14 Hong Hu , Yue M. Lu , Theodor Misiakiewicz

The relationship between a time-dependent covariate and survival times is usually evaluated via the Cox model. Time-dependent covariates are generally available as longitudinal data collected regularly during the course of the study. A…

Statistics Theory · Mathematics 2007-06-13 Jean-François Dupuy , Ion Grama , Mounir Mesbah

In Selk and Gertheiss (2022) a nonparametric prediction method for models with multiple functional and categorical covariates is introduced. The dependent variable can be categorical (binary or multi-class) or continuous, thus both…

Statistics Theory · Mathematics 2023-04-04 Leonie Selk

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 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

Supervised learning by extreme learning machines resp. neural networks with random weights is studied under a non-stationary spatial-temporal sampling design which especially addresses settings where an autonomous object moving in a…

Machine Learning · Statistics 2021-09-02 Ansgar Steland

Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…

Methodology · Statistics 2023-08-08 Sagnik Bhadury , Riten Mitra , Jeremy T. Gaskins

In randomized clinical trials, adjustments for baseline covariates at both design and analysis stages are highly encouraged by regulatory agencies. A recent trend is to use a model-assisted approach for covariate adjustment to gain…

Methodology · Statistics 2021-07-14 Ting Ye , Jun Shao , Yanyao Yi , Qingyuan Zhao

We give two asymptotic results for the empirical distance covariance on separable metric spaces without any iid assumption on the samples. In particular, we show the almost sure convergence of the empirical distance covariance for any…

Probability · Mathematics 2021-01-07 Marius Kroll

Large-margin classifiers are popular methods for classification. We derive the asymptotic expression for the generalization error of a family of large-margin classifiers in the limit of both sample size $n$ and dimension $p$ going to…

Machine Learning · Statistics 2020-12-02 Hanwen Huang , Qinglong Yang

Conditional copula models allow dependence structures to vary with observed covariates while preserving a separation between marginal behavior and association. We study the uniform asymptotic behavior of kernel-weighted local likelihood…

Statistics Theory · Mathematics 2026-01-06 Mathias Nthiani Muia

This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…

Statistics Theory · Mathematics 2008-02-20 Joseph Rynkiewicz

The assumption of Gaussian or Gaussian mixture data has been extensively exploited in a long series of precise performance analyses of machine learning (ML) methods, on large datasets having comparably numerous samples and features. To…

Machine Learning · Statistics 2025-03-14 Xiaoyi Mai , Zhenyu Liao

In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…

Statistics Theory · Mathematics 2021-02-11 Leonie Selk , Charles Tillier , Orlando Marigliano

Random fields play a central role in the analysis of spatially correlated data and, as a result, have a significant impact on a broad array of scientific applications. This paper studies the cepstral random field model, providing recursive…

Statistics Theory · Mathematics 2014-01-17 Tucker S. McElroy , Scott H. Holan

Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…

Machine Learning · Statistics 2025-08-26 Yuta Shikuri

This paper develops a general asymptotic theory for nonparametric kernel regression in the presence of cluster dependence. We examine nonparametric density estimation, Nadaraya-Watson kernel regression, and local linear estimation. Our…

Econometrics · Economics 2024-12-31 Yuya Shimizu

We provide exact asymptotic expressions for the performance of regression by an $L-$layer deep random feature (RF) model, where the input is mapped through multiple random embedding and non-linear activation functions. For this purpose, we…

Machine Learning · Statistics 2023-02-14 David Bosch , Ashkan Panahi , Babak Hassibi

This paper studies large sample properties of a Bayesian approach to inference about slope parameters $\gamma$ in linear regression models with a structural break. In contrast to the conventional approach to inference about $\gamma$ that…

Econometrics · Economics 2023-08-15 Kenichi Shimizu