Effective sample size for georeferenced and temporally evolving data

The effective sample size (ESS) measures the number of inde-pendent observations within a sample. This quantity has been studied and applied in many branches of statistics in recent years. In particular, it is used in the statistical analysis of spatial data for detecting duplicated observations as a consequence of the spatial correlation that is typically encountered in prac-tice, allowing for subsequent model-informed data reduction procedures. The primary goal of this article is to introduce a space-time ESS, extending the current literature from the purely spatial to the space-time setting. The proposed ESS can be broken down into spatial and temporal margins. Thus, a statistician could perform purely spatial, purely temporal or joint space-time data reductions in such a way that the simultaneous space-time dependency structure is honored. We show that several elementary attributes that have been widely studied for the purely spatial ESS can translate naturally to the space-time context. We also present some results that connect the proposed ESS with the property of non-separability between space and time. After presenting our results, we apply them to a real data set consisting of daily averages of wind speeds in Ireland dur-ing 1961-1978. We obtain that, at each meteorological station, the sample size could be reduced by 80%, while maintaining critical statistical information of the data, demonstrating the effectiveness of our proposal.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

The effective sample size (ESS) is a measure of independent observations within a sample and has been extensively studied and applied in various statistical fields. This article introduces a space-time ESS, extending the current literature from pure spatial settings to the space-time context. The proposed ESS can be decomposed into spatial and temporal components, allowing statisticians to perform spatial, temporal, or joint space-time data reductions while preserving the simultaneous space-time dependency structure. The results demonstrate the natural translation of elementary attributes from purely spatial ESS to the space-time context and establish connections between the proposed ESS and the non-separability of space and time. Applied to a real wind speed dataset, the proposed ESS reduces the sample size by 80% while maintaining critical statistical information.