Threshold Exceedance Estimation in Spatially Correlated Areal Data Using Maxima-Nominated Sampling

TL;DR

This paper introduces a novel sampling design for estimating the proportion of high-risk spatial units, combining maxima-nominated sampling with probability-proportional-to-size techniques, and demonstrates its advantages through theoretical analysis and real data application.

Contribution

It develops the DUST-MNS sampling method, providing a closed-form estimator, bias and variance analysis, and practical guidance for spatial exceedance estimation.

Findings

DUST-MNS estimator outperforms SRS and DUST-SRS in certain regimes

Provides bias, variance, and efficiency bounds for the estimator

Application to CDC stroke prevalence data demonstrates practical utility

Abstract

We study estimation of the proportion of areal units in a spatially correlated domain whose success probabilities exceed a prespecified threshold. Such problems arise in health surveillance, environmental monitoring, and social policy, where the goal is to estimate the fraction of high-risk areas. We propose a DUST-MNS design that combines maxima-nominated sampling (MNS) with the probability-proportional-to-size dependent unit sequential technique (pps-DUST), thereby promoting spatial spread while mitigating the effect of spatial autocorrelation. The design forms $n$ candidate sets of size $k$ and obtains final measurements only from the area judged to be at highest risk in each set, yielding $n$ measured areas from $nk$ screened candidates. Ranking may be based on expert judgment, prior surveys, or easily obtained auxiliary covariates. We derive a closed-form estimator of the exceedance probability $\theta$ based on data from DUST-MNS design, establish its bias and variance, and show that, in the rare-to-moderate exceedance regime $\theta<\theta^\star(k)$, the proposed DUST-MNS estimator outperforms its SRS and DUST-SRS counterparts, where $\theta^\star(k)$ depends only on $k$. We also provide guidance on the choice of $k$, derive efficiency bounds under a Beta model, extend the method to imperfect ranking, and develop variance estimation and bootstrap confidence intervals. An application to county-level stroke prevalence data from CDC PLACES, using diabetes prevalence as the ranking concomitant, illustrates the proposed approach.