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Statistical methods for inference on spatial extremes of large datasets are yet to be developed. Motivated by standard dimension reduction techniques used in spatial statistics, we propose an approach based on empirical basis functions to…

Methodology · Statistics 2018-08-02 Samuel A. Morris , Brian J. Reich , Emeric Thibaud

We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the `space' being of a general economic or social nature. Dependence can be parametric, parametric with increasing…

Econometrics · Economics 2022-08-30 Abhimanyu Gupta , Xi Qu

Linear quantile regression is a powerful tool to investigate how predictors may affect a response heterogeneously across different quantile levels. Unfortunately, existing approaches find it extremely difficult to adjust for any dependency…

Methodology · Statistics 2019-10-30 Xu Chen , Surya T. Tokdar

Analyzing the covariance structure of data is a fundamental task of statistics. While this task is simple for low-dimensional observations, it becomes challenging for more intricate objects, such as multivariate functions. Here, the…

Methodology · Statistics 2023-01-12 Holger Dette , Gauthier Dierickx , Tim Kutta

We prove weak convergence in a separable Hilbert space for estimators of high-dimensional regression coefficients, which yields asymptotic normality and enables direct use of standard asymptotic tools such as the continuous mapping theorem.…

Statistics Theory · Mathematics 2026-05-05 Kou Fujimori , Koji Tsukuda

Given a positive definite, bounded linear operator $A$ on the Hilbert space $\mathcal{H}_0:=l^2(E)$, we consider a reproducing kernel Hilbert space $\mathcal{H}_+$ with a reproducing kernel $A(x,y)$. Here $E$ is any countable set and…

Probability · Mathematics 2007-05-23 Hyun Jae Yoo

This paper proposes a novel scheme for reduced-rank Gaussian process regression. The method is based on an approximate series expansion of the covariance function in terms of an eigenfunction expansion of the Laplace operator in a compact…

Machine Learning · Statistics 2020-06-26 Arno Solin , Simo Särkkä

Regression models with a response variable taking values in a Hilbert space and hybrid covariates are considered. This means two sets of regressors are allowed, one of finite dimension and a second one functional with values in a Hilbert…

Statistics Theory · Mathematics 2014-06-25 Samuel Maistre , Valentin Patilea

In this paper, we study a functional regression setting where the random response curve is unobserved, and only its dichotomized version observed at a sequence of correlated binary data is available. We propose a practical computational…

Methodology · Statistics 2020-12-07 Fatemeh Asgari , Mohammad Hossein Alamatsaz , Valeria Vitelli , Saeed Hayati

Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering.Such measurements can be viewed as…

In this article, we consider convergence rates in functional linear regression with functional responses, where the linear coefficient lies in a reproducing kernel Hilbert space (RKHS). Without assuming that the reproducing kernel and the…

Methodology · Statistics 2012-11-20 Heng Lian

This paper investigates the modeling of an important class of degradation data, which are collected from a spatial domain over time; for example, the surface quality degradation. Like many existing time-dependent stochastic degradation…

Methodology · Statistics 2017-12-29 Xiao Liu , Kyongmin Yeo , Jayant Kalagnanam

The paper revisits the $\alpha$--regression framework for compositional data. The model uses a flexible power transformation parameterized by $\alpha$ to interpolate between raw data analysis and log--ratio methods, naturally handling zeros…

Methodology · Statistics 2026-05-14 Michail Tsagris , Yannis Pantazis

We study estimation and prediction in linear models where the response and the regressor variable both take values in some Hilbert space. Our main objective is to obtain consistency of a principal components based estimator for the…

Statistics Theory · Mathematics 2014-04-17 Siegfried Hörmann , Łukasz Kidziński

We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…

Statistics Theory · Mathematics 2022-08-24 Daren Wang , Zifeng Zhao , Yi Yu , Rebecca Willett

We present a general theory to quantify the uncertainty from imposing structural assumptions on the second-order structure of nonstationary Hilbert space-valued processes, which can be measured via functionals of time-dependent spectral…

Statistics Theory · Mathematics 2023-09-19 Anne van Delft , Holger Dette

We consider a reproducing kernel Hilbert space of discrete entire functions on the square lattice $\mathbb Z^2$ inspired by the classical Paley-Wiener space of entire functions of exponential growth in the complex plane. For such space we…

Complex Variables · Mathematics 2025-07-15 Alessandro Monguzzi , Matteo Monti

Modelling the extremal dependence structure of spatial data is considerably easier if that structure is stationary. However, for data observed over large or complicated domains, non-stationarity will often prevail. Current methods for…

Methodology · Statistics 2021-03-04 Jordan Richards , Jennifer L. Wadsworth

In spatio-temporal analysis, we often record data at specific time intervals but with varying spatial locations between these timepoints. We propose a conditional model to analyze such spatio-temporal data that accommodates the dependencies…

Methodology · Statistics 2026-04-03 Subhrajyoty Roy , Soudeep Deb , Sayar Karmakar , Rishideep Roy

Function-on-function linear regression is important for understanding the relationship between the response and the predictor that are both functions. In this article, we propose a reproducing kernel Hilbert space approach to…

Statistics Theory · Mathematics 2021-09-29 Holger Dette , Jiajun Tang