Series ridge regression for spatial data on $\mathbb{R}^d$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916634330923008 |
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| author | Kurisu, Daisuke Matsuda, Yasumasa |
| author_facet | Kurisu, Daisuke Matsuda, Yasumasa |
| contents | This paper develops a general asymptotic theory of series estimators for spatial data collected at irregularly spaced locations within a sampling region $R_n \subset \mathbb{R}^d$. We employ a stochastic sampling design that can flexibly generate irregularly spaced sampling sites, encompassing both pure increasing and mixed increasing domain frameworks. Specifically, we focus on a spatial trend regression model and a nonparametric regression model with spatially dependent covariates. For these models, we investigate $L^2$-penalized series estimation of the trend and regression functions. We establish uniform and $L^2$ convergence rates and multivariate central limit theorems for general series estimators as main results. Additionally, we show that spline and wavelet series estimators achieve optimal uniform and $L^2$ convergence rates and propose methods for constructing confidence intervals for these estimators. Finally, we demonstrate that our dependence structure conditions on the underlying spatial processes cover a broad class of random fields, including Lévy-driven continuous autoregressive and moving average random fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02773 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Series ridge regression for spatial data on $\mathbb{R}^d$ Kurisu, Daisuke Matsuda, Yasumasa Statistics Theory Methodology This paper develops a general asymptotic theory of series estimators for spatial data collected at irregularly spaced locations within a sampling region $R_n \subset \mathbb{R}^d$. We employ a stochastic sampling design that can flexibly generate irregularly spaced sampling sites, encompassing both pure increasing and mixed increasing domain frameworks. Specifically, we focus on a spatial trend regression model and a nonparametric regression model with spatially dependent covariates. For these models, we investigate $L^2$-penalized series estimation of the trend and regression functions. We establish uniform and $L^2$ convergence rates and multivariate central limit theorems for general series estimators as main results. Additionally, we show that spline and wavelet series estimators achieve optimal uniform and $L^2$ convergence rates and propose methods for constructing confidence intervals for these estimators. Finally, we demonstrate that our dependence structure conditions on the underlying spatial processes cover a broad class of random fields, including Lévy-driven continuous autoregressive and moving average random fields. |
| title | Series ridge regression for spatial data on $\mathbb{R}^d$ |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/2402.02773 |