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：比较农业田地空间参考下的多元产量质量分布时，常受非正态性和空间自相关这两个普遍特征的影响。ANOVA、MANOVA等经典方法及标准秩检验假设样本独立，因此在存在空间依赖时会出现严重的I类错误膨胀。我们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，该过程由混合分量秩构建而成。空间核权重明确处理局部依赖关系，而秩变换消除了对边缘分布形式的敏感性。在固定域填充渐近性和多项式α-混合条件下，我们证明了平滑经验copula过程弱收敛于零均值高斯极限，且所得二次型检验统计量收敛于受限在K-1维对比子空间上的加权卡方随机变量和。通过高斯copula模型下精确离散空间协方差算子校准的Satterthwaite近似实现实际推断。采用双变量对数正态空间数据的蒙特卡洛实验表明，与严重非保守的经典参数方法及非空间秩方法相比，本检验在不同强度空间依赖下均能保持名义检验水平。该程序为精准农业及相关应用领域中多元空间产量分布的统计比较提供了理论严谨且计算可行的框架。