A0371
Title: Series ridge regression for spatial data
Authors: Daisuke Kurisu - The University of Tokyo (Japan) [presenting]
Yasumasa Matsuda - Tohoku University (Japan)
Abstract: A general asymptotic theory of series estimators is developed for spatial data collected at irregularly spaced locations within a sampling region. A stochastic sampling design is employed that can flexibly generate irregularly spaced sampling sites, encompassing both pure increasing and mixed increasing domain frameworks. Specifically, the focus is on a spatial trend regression model and a nonparametric regression model with spatially dependent covariates. For these models, L2-penalized series estimation of the trend and regression functions is investigated. Uniform and L2 convergence rates and multivariate central limit theorems are established for general series estimators as the main results. Additionally, it is shown that spline and wavelet series estimators achieve optimal uniform and L2 convergence rates and propose methods for constructing confidence intervals for these estimators. Finally, the dependence structure conditions on the underlying spatial processes include a broad class of random fields, including Levy-driven continuous autoregressive and moving average random fields.
