Properties of design-based estimation under stratified spatial sampling with application to canopy coverage estimation

TL;DR

This paper analyzes a stratified spatial sampling scheme for estimating continuous attributes like canopy coverage, demonstrating its unbiasedness, efficiency, and normality properties, with practical implications for environmental surveys.

Contribution

It introduces and evaluates a stratified sampling scheme that improves estimation efficiency and provides theoretical guarantees for unbiasedness and normality.

Findings

The scheme yields unbiased estimators.

It is 'superefficient' compared to uniform sampling.

Large-sample normality is established.

Abstract

The estimation of the total of an attribute defined over a continuous planar domain is required in many applied settings, such as the estimation of canopy coverage in the Monterano Nature Reserve in Italy. If the design-based approach is considered, the scheme for the placement of the sample sites over the domain is fundamental in order to implement the survey. In real situations, a commonly adopted scheme is based on partitioning the domain into suitable strata, in such a way that a single sample site is uniformly placed (i.e., selected with uniform probability density) in each stratum and sample sites are independently located. Under mild conditions on the function representing the target attribute, it is shown that this scheme gives rise to an unbiased spatial total estimator which is "superefficient" with respect to the estimator based on the uniform placement of independent sample sites over the domain. In addition, the large-sample normality of the estimator is proven and variance estimation issues are discussed.