A double fixed rank kriging approach to spatial regression models with covariate measurement error

Abstract

In many applications of spatial regression modeling, the spatially indexed covariates are measured with error, and it is known that ignoring this measurement error can lead to attenuation of the estimated regression coefficients. Classical measurement error techniques may not be appropriate in the spatial setting, due to the lack of validation data and the presence of (residual) spatial correlation among the responses. In this article, we propose a double fixed rank kriging (FRK) approach to obtain bias‐corrected estimates of and inference on coefficients in spatial regression models, where the covariates are spatially indexed and subject to measurement error. Assuming they vary smoothly in space, the proposed method first fits an FRK model regressing the covariates against spatial basis functions to obtain predictions of the error‐free covariates. These are then passed into a second FRK model, where the response is regressed against the predicted covariates plus another set of spatial basis functions to account for spatial correlation. A simulation study and an application to presence–absence records of Carolina wren from the North American Breeding Bird Survey demonstrate that the proposed double FRK approach can be effective in adjusting for measurement error in spatially correlated data.

Evaluation of GPM IMERG Satellite Precipitation Products in Event-Based Flood Modeling over the Sunshui River Basin in Southwestern China

“…The commonly used methods for bias correction of satellite rainfall data include linear regression, mean bias correction, Bayesian fusion, geographically weighted regression, and geographic differential analysis (GDA) [24,[33][34][35]. We selected the GDA method to correct the GPM IMERG rainfall data due to its superior correction performance and simple application [36].…”

Environmental data science: Part 1

“…The big‐models‐big‐data setting leads to the consideration of statistical computing, and this is also reflected in the special issue. Low‐rank representations of process models are often used to address the problem of high dimensionality, and this is the approach taken by Kleiber et al (2023) in the context of circular processes, and by Ning et al (2023), who use resolution‐adaptive basis functions for modeling both the covariates and the spatial process of interest. Basis‐function expansions also feature in the discussion of Rougier et al (2023).…”

“…Temporal, spatial and spatio‐temporal models are central to the vast majority of contributions to the issue. Lowther et al (2023) consider multiple time series data that contain change points, and showcase their methods on data on the Greenland ice sheet; Kleiber et al (2023) consider the problem of modeling and simulating tropical cyclone precipitation fields using a spatio‐temporal model in polar coordinates; Shirota et al (2023) tackle the problem of fitting spatial models to light detection and ranging (LiDAR) data collected over Alaska; Abdulah et al (2023) consider the spatial analysis of sea‐surface temperature data; Jurek and Katzfuss (2023) the spatio‐temporal analysis of total precipitable water; Daw and Wikle (2023) the spatial analysis of satellite temperature data; Ning et al (2023) the spatial analysis of presence‐absence ecological data; and the discussion by Rougier et al (2023) focuses on the challenges of fitting spatio‐temporal models to environmental data. The large number of contributed papers involving these classes of models is not coincidental, as many of the phenomena that are analyzed in EDS are temporal, spatial or spatio‐temporal in nature.…”

Reconstructing global daily XCO2 at 1° × 1° spatial resolution from 2016 to 2019 with multisource satellite observation data

“…This makes it suitable for analyzing massive spatial data. [23][24][25] The goal of this study is to obtain the spatiotemporal continuous global daily XCO 2 dataset on grids of 1°and analyze the spatiotemporal variations from GOSAT, OCO-2, and OCO-3 satellite XCO 2 data. Due to the differences in the and noise level among different satellites, the traditional FRK methods cannot be ideally applied to multisource satellite data.…”