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A Rank-Based Test for Comparing Multiple Fields' Yield Quality Distributions Under Spatial Dependence

Marco Mandap

Abstract

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.

A Rank-Based Test for Comparing Multiple Fields' Yield Quality Distributions Under Spatial Dependence

Abstract

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 -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.
Paper Structure (45 sections, 5 theorems, 95 equations, 2 tables)

This paper contains 45 sections, 5 theorems, 95 equations, 2 tables.

Table of Contents

  1. Introduction
  2. The Challenge of Spatial Yield Data
  3. Existing Approaches and Their Limitations
  4. The Proposed Solution
  5. Methodology
  6. Statistical Model and Notation
  7. Spatial dependence.
  8. Kernel-Smoothed Empirical Distribution Function
  9. Effective local sample size and normalization.
  10. Contrast Processes and Test Statistic
  11. Correct scaling for between-field contrasts.
  12. Test statistic.
  13. How Spatial Dependence Enters the Limit
  14. Practical Inference via the Satterthwaite Approximation
  15. Algorithm for Computing the p-value
  16. ...and 30 more sections

Key Result

Lemma 1

Assume $H_0$ so that $F_k\equiv F$, and assume the field $\{X_{k,\mathbf s}\}$ is strictly stationary and $\alpha$-mixing with $\alpha(r)\le Cr^{-\theta}$ for some $\theta>d(2+\delta)/\delta$ and some $\delta>0$. For fixed $x,y\in\mathbb R$, where The integral converges absolutely.

Theorems & Definitions (9)

  • Lemma 1: Asymptotic covariance under fixed-bandwidth infill
  • proof
  • Lemma 2: Finite-dimensional convergence of $\widetilde{\mathbb G}_{n,k}$
  • proof
  • Lemma 3: Tightness
  • proof
  • Theorem 1: Weak convergence of $\widetilde{\mathbb G}_{n,k}$
  • Theorem 2: Asymptotic null distribution (local-infill)
  • proof : Proof of Theorem \ref{['thm:asymp_local']}