标题： 复杂调查设计的最小Hellinger距离估计量 显示英文标题

标题： Minimum Hellinger Distance Estimators for Complex Survey Designs

摘要： 从复杂调查样本中得出可靠的推断可能会受到异常值和高杠杆观测值的干扰，这些异常值和高杠杆观测值是由不等的纳入概率和校准引起的。 我们开发了一种最小Hellinger距离估计量（MHDE），用于复杂设计下的参数超总体模型，包括泊松PPS和固定大小的SRS/PPS无放回抽样，可能具有随机后分层或校准权重。 使用一个Horvitz-Thompson调整的核密度插值，我们证明了：(i) KDE的$L^1$-一致性，具有由方差自适应有效样本量驱动的显式大偏差尾部界限；(ii) Hellinger相似性的均匀指数界限，这在较弱的可识别性条件下产生MHDE的一致性；(iii) MHDE的渐近正态分布，协方差为$\mathbf A^{-1}\boldsymbol\Sigma \mathbf A^{\intercal}$（在无放回设计下有有限总体修正）；以及(iv) 通过Hellinger拓扑中的影响函数和$\alpha$-影响曲线实现稳健性。 在Gamma和对数正态超总体模型下的模拟量化了相对于独立和高杠杆污染下加权MLE的效率-稳健性权衡。 对NHANES 2021-2023总水分摄入的应用表明，尽管存在极端响应，MHDE仍然保持稳定，而MLE则明显被偏差。 该估计量可以通过在固定网格上进行数值积分来简单实现，并且可以扩展到其他散度族。 显示英文摘要

摘要： Reliable inference from complex survey samples can be derailed by outliers and high-leverage observations induced by unequal inclusion probabilities and calibration. We develop a minimum Hellinger distance estimator (MHDE) for parametric superpopulation models under complex designs, including Poisson PPS and fixed-size SRS/PPS without replacement, with possibly stochastic post-stratified or calibrated weights. Using a Horvitz-Thompson-adjusted kernel density plug-in, we show: (i) $L^1$-consistency of the KDE with explicit large-deviation tail bounds driven by a variance-adaptive effective sample size; (ii) uniform exponential bounds for the Hellinger affinity that yield MHDE consistency under mild identifiability; (iii) an asymptotic Normal distribution for the MHDE with covariance $\mathbf A^{-1}\boldsymbol\Sigma \mathbf A^{\intercal}$ (and a finite-population correction under without-replacement designs); and (iv) robustness via the influence function and $\alpha$-influence curves in the Hellinger topology. Simulations under Gamma and lognormal superpopulation models quantify efficiency-robustness trade-offs relative to weighted MLE under independent and high-leverage contamination. An application to NHANES 2021-2023 total water consumption shows that the MHDE remains stable despite extreme responses that markedly bias the MLE. The estimator is simple to implement via quadrature over a fixed grid and is extensible to other divergence families.