Comparing yield quality distributions across multiple agricultural fields is fundamental for evaluating management practices, yet it is complicated by two pervasive data characteristics: non-normality and spatial autocorrelation. Traditional parametric tests, such as ANOVA, frequently suffer from severe Type I error inflation when the independence assumption is violated by spatial dependence. This paper introduces a novel rank-based test framework that utilizes spatial kernel smoothing to construct robust empirical distribution functions (EDFs). We establish the asymptotic properties of the test statistic under $α$-mixing conditions, proving its convergence to a weighted sum of chi-squared random variables. To facilitate practical inference, we employ a Satterthwaite approximation to derive effective degrees of freedom that account for the spatial 'inflation' of variance. The theoretical framework is developed in detail, providing a rigorous foundation for the proposed method. Simulation studies and applications to real yield quality data are left to future work.

翻译：比较多个农田的产量质量分布是评估管理实践的基础，但普遍存在的两个数据特征——非正态性和空间自相关性——使这一任务变得复杂。当空间依赖性违背独立性假设时，传统的参数检验方法（如方差分析）常出现严重的Ⅰ类错误膨胀。本文提出了一种新颖的基于秩的检验框架，该框架利用空间核平滑构建稳健的经验分布函数。我们在α混合条件下建立了检验统计量的渐近性质，证明其收敛于加权卡方随机变量之和。为便于实际推断，我们采用萨特思韦特近似来推导有效自由度，以解释方差的空间“膨胀”。本文详细阐述了理论框架，为所提方法提供了严谨的基础。模拟研究及在真实产量质量数据中的应用将留待后续工作。