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：比较多个农业田地的产量质量分布是评估管理实践的基础，但这一过程常因两个普遍存在的数据特征——非正态性和空间自相关——而变得复杂。传统参数检验（如方差分析）在空间依赖违背独立性假设时，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次的检验框架，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，证明其收敛于卡方随机变量的加权和。为促进实际推断，我们采用Satterthwaite近似推导了考虑空间方差膨胀效应的有效自由度。本文详细阐述了理论框架，为所提方法提供了严格的理论基础。模拟研究及实际产量质量数据的应用留待未来工作完成。