Nearest-neighbour methods based on first differences are an approach to spatial analysis of field trials with a long history, going back to the early work by Papadakis first published in 1937. These methods are closely related to a geostatistical model that assumes spatial covariance to be a linear function of distance. Recently, P-splines have been proposed as a flexible alternative to spatial analysis of field trials. On the surface, P-splines may appear like a completely new type of method, but closer scrutiny reveals intimate ties with earlier proposals based on first differences and the linear variance model. This paper studies these relations in detail, first focussing on one-dimensional spatial models and then extending to the two-dimensional case. Two yield trial datasets serve to illustrate the methods and their equivalence relations. Parsimonious linear variance and random walk models are suggested as a good point of departure for exploring possible improvements of model fit via the flexible P-spline framework.

中文翻译：

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现场试验中空间调整的线性方差、P 样条和邻域差异：它们之间有什么关系？

基于一阶差分的最近邻方法是一种历史悠久的田间试验空间分析方法，可以追溯到 Papadakis 于 1937 年首次发表的早期工作。这些方法与假设空间协方差为距离的线性函数。最近，已提出 P 样条作为现场试验空间分析的灵活替代方案。从表面上看，P 样条可能看起来像是一种全新的方法，但更仔细的审查揭示了与早期基于一阶差分和线性方差模型的提议的密切联系。本文详细研究了这些关系，首先关注一维空间模型，然后扩展到二维情况。两个产量试验数据集用于说明方法及其等价关系。