Electronic Journal of Statistics

Estimation of the mean for spatially dependent data belonging to a Riemannian manifold

Davide Pigoli and Piercesare Secchi

Full-text: Open access

Abstract

The statistical analysis of data belonging to Riemannian manifolds is becoming increasingly important in many applications. The aim of this work is to introduce models for spatial dependence among Riemannian data, with a special focus on the case of positive definite symmetric matrices. First, the Riemannian semivariogram of a field of positive definite symmetric matrices is defined. Then, we propose an estimator for the mean which considers both the non Euclidean nature of the data and their spatial correlation. Simulated data are used to evaluate the performance of the proposed estimator: taking into account spatial dependence leads to better estimates when observations are irregularly spaced in the region of interest. Finally, we address a meteorological problem, namely, the estimation of the covariance matrix between temperature and precipitation for the province of Quebec in Canada.

Article information

Source
Electron. J. Statist., Volume 6 (2012), 1926-1942.

Dates
First available in Project Euclid: 12 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1350046858

Digital Object Identifier
doi:10.1214/12-EJS733

Mathematical Reviews number (MathSciNet)
MR2988469

Zentralblatt MATH identifier
1295.62055

Subjects
Primary: 62H11: Directional data; spatial statistics
Secondary: 62H12: Estimation

Keywords
Non Euclidean data semivariogram Fréchet mean meteorological data

Citation

Pigoli, Davide; Secchi, Piercesare. Estimation of the mean for spatially dependent data belonging to a Riemannian manifold. Electron. J. Statist. 6 (2012), 1926--1942. doi:10.1214/12-EJS733. https://projecteuclid.org/euclid.ejs/1350046858


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