# Nonparametric Spectral Methods for Multivariate Spatial and Spatial-Temporal Data

arXiv: https://arxiv.org/abs/1811.01280 · HTML: https://mlsanity.com/paper/1811.01280/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2018.

## Built on by (most cited first, 1 of 1)

- [Modeling massive highly-multivariate nonstationary spatial data with the basis graphical lasso](https://mlsanity.com/paper/2101.02404/) (2021)

## Abstract (arXiv)

We propose computationally efficient methods for estimating stationary multivariate spatial and spatial-temporal spectra from incomplete gridded data. The methods are iterative and rely on successive imputation of data and updating of model estimates. Imputations are done according to a periodic model on an expanded domain. The periodicity of the imputations is a key feature that reduces edge effects in the periodogram and is facilitated by efficient circulant embedding techniques. In addition, we describe efficient methods for decomposing the estimated cross spectral density function into a linear model of coregionalization plus a residual process. The methods are applied to two storm datasets, one of which is from Hurricane Florence, which struck the souteastern United States in September 2018. The application demonstrates how fitted models from different datasets can be compared, and how the methods are computationally feasible on datasets with more than 200,000 total observations.