发表机构
Rutgers University（罗格斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对空间平衡抽样中方差估计的难题，提出基于蒙特卡洛修正和模型辅助自助法的两种方法，后者性能更稳定，二者具有互补优势。
AI 中文摘要
空间平衡抽样设计，如局部关键方法（LPM），能够改善辅助变量空间的代表性，但基于设计的方差估计具有挑战性，因为二阶包含概率通常难以处理，并且可能为零或接近于零。我们提出了两种方法来估计霍维茨-汤普森均值和有限总体方差的方差。第一种方法通过蒙特卡洛模拟估计联合包含概率，并使用成对独立性检验来修正所得的方差估计量。第二种方法，即模型辅助自助法（MABS），利用插值高斯过程构建一个合成有限总体，并在原始LPM设计下通过重抽样来估计方差。在模拟中，当响应与辅助变量强相关时，修正的经验方法表现良好，但随着这种关联减弱，其对霍维茨-汤普森均值的性能会下降。MABS在不同噪声水平和抽样设置（包括LPM2和非高斯噪声）下表现出更稳定的性能。然而，对于有限总体方差估计，没有方法显示出统一的优势。这些结果说明了所提方法在空间平衡抽样下进行推断的互补优势。
英文摘要
Spatially balanced sampling designs, such as the local pivotal methods (LPM), improve representation of auxiliary-variable space, but design-based variance estimation is challenging because second-order inclusion probabilities are generally intractable and may be zero or near zero. We propose two approaches for estimating the variance of the Horvitz-Thompson mean and the finite-population variance. The first estimates joint inclusion probabilities by Monte Carlo simulation and uses pairwise independence tests to modify the resulting variance estimators. The second, a model-assisted bootstrap (MABS), uses an interpolating Gaussian process to construct a synthetic finite population and estimates variance by resampling under the original LPM design. In simulations, the modified empirical approach performs well when responses are strongly associated with auxiliary variables, but its performance for the Horvitz-Thompson mean deteriorates as this association weakens. MABS exhibits more stable performance across noise levels and sampling settings, including under LPM2 and non-Gaussian noise. For finite-population variance estimation, however, no method shows a uniform advantage. These results illustrate the complementary strengths of the proposed approaches for inference under spatially balanced sampling.
Comments25 pages, 4 figures
