In survey domain estimation, a priori information can often be imposed in the form of linear inequality constraints on the domain estimators. Wu et al. (2016) formulated the isotonic domain mean estimator, for the simple order restriction, and methods for more general constraints were proposed in Oliva-Avilés et al. (2020). When the assumptions are valid, imposing restrictions on the estimators will ensure that the a priori information is respected, and in addition allows information to be pooled across domains, resulting in estimators with smaller variance. Here, we propose a method to further improve the estimation of the covariance matrix for these constrained domain estimators, using a mixture of possible covariance matrices obtained from the inequality constraints. We prove consistency of the improved variance estimator, and simulations demonstrate that the new estimator results in improved coverage probabilities for domain mean confidence intervals, while retaining the smaller confidence interval lengths.

在调查域估计中，先验信息通常可以以线性不等式约束的形式强加于域估计器上。Wu等。（2016年）制定了等渗域均值估计器，用于简单的顺序限制，并在Oliva-Avilés等人（2014年）中提出了用于更一般性限制的方法。（2020）。当假设有效时，对估计量施加限制将确保先验尊重信息，此外还允许跨域合并信息，从而使估计量的方差较小。在这里，我们提出了一种方法，该方法使用从不等式约束中获得的可能协方差矩阵的混合，进一步改善这些受约束域估计量的协方差矩阵的估计。我们证明了改进的方差估计量的一致性，并且仿真表明，新的估计量可提高域平均置信区间的覆盖概率，同时保留较小的置信区间长度。