Comparing multivariate yield quality distributions across spatially referenced agricultural fields is complicated by two pervasive features: non-normality and spatial autocorrelation. Classical procedures such as ANOVA, MANOVA, and standard rank tests assume independence and therefore exhibit severe Type I error inflation when spatial dependence is present. We propose a nonparametric spatial Cramer-von Mises-type test based on kernel-smoothed empirical copula processes constructed from pooled componentwise ranks. Spatial kernel weights account explicitly for local dependence, while the rank transformation removes sensitivity to marginal distributional form. Under fixed-domain infill asymptotics and polynomial alpha-mixing conditions, we establish weak convergence of the smoothed empirical copula process to a mean-zero Gaussian limit and show that the resulting quadratic test statistic converges to a weighted sum of chi-squared random variables restricted to the K-1-dimensional contrast subspace. Practical inference is obtained through a Satterthwaite approximation calibrated using the exact discrete spatial covariance operator under a Gaussian copula model. Monte Carlo experiments with bivariate log-normal spatial data demonstrate that the proposed test maintains nominal size across varying strengths of spatial dependence, in contrast to classical parametric and non-spatial rank-based methods, which become severely anti-conservative. The procedure provides a theoretically justified and computationally tractable framework for comparing multivariate spatial yield distributions in precision agriculture and related applied settings.

翻译：比较空间参考农田间的多元产量质量分布面临两个普遍存在的特征挑战：非正态性和空间自相关性。经典方法如ANOVA、MANOVA及标准秩检验均假设独立性，因此在存在空间依赖性时会出现严重的I类错误膨胀。本文提出一种基于核平滑经验Copula过程的非参数空间Cramer-von Mises型检验，该过程通过合并分量秩构建而成。空间核权重显式处理局部依赖性，而秩变换则消除了对边缘分布形式的敏感性。在固定域填充渐近性与多项式α混合条件下，我们建立了平滑经验Copula过程向零均值高斯极限的弱收敛性，并证明所得二次检验统计量收敛于限制在K-1维对比子空间上的加权卡方随机变量和。实际推断通过Satterthwaite近似获得，该近似采用高斯copula模型下的精确离散空间协方差算子进行校准。对双变量对数正态空间数据的蒙特卡洛实验表明，相较于经典参数化方法和非空间秩基方法（这些方法会变得严重反保守），所提检验能在不同空间依赖强度下保持名义检验水平。该方法为精准农业及相关应用场景中多元空间产量分布的比较提供了理论依据充分且计算可行的框架。