Estimating proportion of area from a stratified random sample and reference class labels obtained by ground visit or interpretation of satellite imagery is a common strategy in land cover monitoring. Confidence intervals for the proportion of area are typically estimated using the Wald interval, a procedure that is known to yield less than nominal coverage (i.e., undercoverage) when the proportion of area is small (i.e., comprising 10% or less of the region of interest). The practical implication of undercoverage is that confidence intervals will include the true proportion of area for a smaller percent of samples than is implied by the stated confidence level (e.g., 95%). For simple random sampling, alternate confidence interval methods such as Wilson, Agresti-Coull, and Clopper-Pearson have been developed to remedy the undercoverage of the Wald interval, but these methods are not directly applicable to stratified sampling. In this study, we evaluated the Wald interval and two alternative general confidence interval approaches for the case of two strata. One alternative approach, previously proposed in the literature, is based on estimating effective sample size (neff method), whereas the other approach is a new method based on summing stratum-specific confidence bounds (sumstrat method) computed using one of the alternate confidence interval approaches (Wilson, Agresti-Coull, and Clopper-Pearson) for each stratum. The coverage and length of confidence intervals estimated from the different methods were compared using Monte Carlo simulation applied to a set of populations representing diverse conditions of prevalence of the target class and user's and producer's accuracies of the map used to construct the strata. The commonly applied Wald interval achieved coverage well below the nominal 95% confidence for many of the populations evaluated, and the neff method improved upon this undercoverage in only a few populations. The Wilson sumstrat intervals provided the best coverage as this method achieved close to the nominal 95% coverage or greater for most populations. Length of the Wilson sumstrat intervals was comparable to length of other methods. Further study is needed to determine which confidence interval methods are effective when the number of strata exceeds two.

从分层随机样本和通过地面访问或卫星图像解释获得的参考类标签估计面积比例是土地覆盖监测中的常用策略。面积比例的置信区间通常使用 Wald 区间进行估计，当面积比例较小（即，包括 10% 或更少的地区兴趣）。覆盖不足的实际含义是，置信区间将包括比规定的置信水平（例如，95%）更小百分比的样本的真实面积比例。对于简单的随机抽样，可以使用其他置信区间方法，例如 Wilson、Agresti-Coull、Clopper-Pearson 和 Clopper-Pearson 已被开发来弥补 Wald 区间的覆盖不足，但这些方法并不直接适用于分层抽样。在本研究中，我们针对两层的情况评估了 Wald 区间和两种可供选择的一般置信区间方法。文献中先前提出的另一种方法是基于估计有效样本量（neff方法），而另一种方法是基于对每个层使用备用置信区间方法之一（Wilson、Agresti-Coull 和 Clopper-Pearson）计算的层特定置信界限（ sumstrat方法）求和的新方法。使用蒙特卡罗模拟比较了从不同方法估计的置信区间的覆盖范围和长度，该模拟应用于代表目标类别的不同流行条件的一组人口以及用于构建地层的地图的用户和生产者的准确性。常用的 Wald 区间对许多被评估人群的覆盖率远低于标称的 95% 置信度，而neff方法仅在少数人群中改善了这种覆盖不足的情况。威尔逊sumstrat区间提供了最佳覆盖率，因为这种方法对大多数人群而言接近标称的 95% 或更高的覆盖率。Wilson sumstrat区间的长度与其他方法的长度相当。需要进一步研究以确定当层数超过两个时哪种置信区间方法有效。