Spatiotemporal Balanced Sampling Design for Longitudinal Area Surveys

Abstract

A spatially balanced sample can produce good estimates of finite population quantities when the study variable is dependent over a spatial region with respect to a superpopulation model. In many longitudinal surveys for monitoring natural resources, annual samples are taken in space to estimate both annual status and annual change. In this paper, we propose a spatiotemporal balanced sampling design with a repeated panel such that the sample for each year is spatially balanced, and the sample combined from consecutive years is also spatially balanced. We propose design-based regression estimators of the annual status and change, and the corresponding variance estimators are also derived. Simulation studies show that the spatial balance of a sample generated by the proposed spatiotemporal balanced sampling design is good, and design-based regression estimators work well. The proposed spatiotemporal balanced sampling design is tested on data from the National Resources Inventory rangeland on-site survey conducted in Texas from 2009 to 2013. For the study variable "average soil aggregate stability," the proposed sampling design and estimators are shown to have better performance compared with the original sample and estimators. Although the spatiotemporal balanced sampling design is proposed in a two-dimensional space, it can be generalized to higher dimensions easily.

Resampling Method for Generalized One-per-Stratum Sampling Designs

“…Grafström et al (2012) proposed two local pivotal methods both performing better than the generalized random tessellation stratified design. Wang and Zhu (2019) proposed a spatio-temporal balanced sampling design based on the local pivotal method. Tillé et al (2018) proposed to use renewal chains and multivariate discrete distributions to tune the joint selection probability of neighboring units to achieve better spatial balance.…”

Estimation of change with partially overlapping and spatially balanced samples

“…In repeated surveys, the monitoring of changes in population totals over time is a common focus in various fields, including environmental and ecological research see, for example, Kalton (1983), Wang and Zhu (2019). Accurately estimating the variance of an estimator of change is crucial for assessing the statistical significance of observed changes (Berger & Priam, 2016).…”