We study estimation of the conditional law $P(Y|X=x)$ and continuous functionals $Ψ(P(Y|X=x))$ when $Y$ takes values in a locally compact Polish space, $X \in \mathbb{R}^p$, and the observations arise from a complex survey design. We propose a survey-calibrated distributional random forest (SDRF) that incorporates complex-design features via a pseudo-population bootstrap, PSU-level honesty, and a Maximum Mean Discrepancy (MMD) split criterion computed from kernel mean embeddings of Hájek-type (design-weighted) node distributions. We provide a framework for analyzing forest-style estimators under survey designs; establish design consistency for the finite-population target and model consistency for the super-population target under explicit conditions on the design, kernel, resampling multipliers, and tree partitions. As far as we are aware, these are the first results on model-free estimation of conditional distributions under survey designs. Simulations under a stratified two-stage cluster design provide finite sample performance and demonstrate the statistical error price of ignoring the survey design. The broad applicability of SDRF is demonstrated using NHANES: We estimate the tolerance regions of the conditional joint distribution of two diabetes biomarkers, illustrating how distributional heterogeneity can support subgroup-specific risk profiling for diabetes mellitus in the U.S. population.

翻译：本研究探讨了当响应变量Y取值于局部紧致波兰空间、协变量X∈ℝ^p，且观测数据来自复杂抽样设计时，条件分布P(Y|X=x)及其连续泛函Ψ(P(Y|X=x))的估计问题。我们提出了一种经过抽样校准的分布随机森林（SDRF）方法，该方法通过伪总体自助法、初级抽样单元层面的诚实性准则，以及基于Hájek型（设计加权）节点分布的核均值嵌入计算的最大均值差异（MMD）分割准则，将复杂设计特征纳入模型构建。我们建立了分析抽样设计下森林类估计量的理论框架，在明确的设计条件、核函数、重抽样乘子及树划分规则下，证明了该方法对有限总体目标的设计相合性以及对超总体目标的模型相合性。据我们所知，这是在抽样设计框架下首次实现条件分布的无模型估计。通过分层两阶段整群抽样设计的模拟实验，我们评估了该方法的有限样本性能，并量化了忽略抽样设计所带来的统计误差代价。利用美国国家健康与营养调查（NHANES）数据，我们展示了SDRF的广泛适用性：通过估计两种糖尿病生物标志物条件联合分布的容忍区域，揭示了分布异质性如何支持美国糖尿病人群亚组特异性风险画像的构建。