arXiv subjects

Marco Mandap

Publications and source records attributed to Marco Mandap.

4 recordsLinked to original sources

arXiv2026

Weak Convergence and Gaussian Limits for a General-Dimensional Origin-Invariant Cram\'er--von Mises Statistic

We introduce a general-dimensional origin-invariant Cram\'er--von Mises statistic $\bar{\omega}_d^2$ for testing complete spatial randomness, defined by averaging corner-oriented empirical-distribution-function discrepancies over all $2^d$ corners of $[0,1]^d$. The statistic has a closed-form $O(n^2)$ computing formula. For $d=1$ it reduces to the classical rank-based Cram\'er--von Mises statistic, while for $d=2$ its computing formula agrees with Zimmerman's origin-invariant statistic. Under iid complete spatial randomness, the associated empirical process converges in $\ell^\infty$ to a centered Gaussian process with an explicit cross-corner covariance kernel. The continuous mapping theorem yields a quadratic Gaussian limit governed by a positive trace-class covariance operator with trace $2^{-d}-3^{-d}$. We also connect fixed-count complete spatial randomness with the homogeneous Poisson formulation. For strictly stationary alpha-mixing sequences with uniform marginals, we establish covariance summability, the long-run variance limit, and a finite-dimensional all-corners Gaussian limit. Monte Carlo experiments illustrate null calibration and sensitivity to selected alternatives. The statistic is consistent against fixed iid alternatives whose distribution functions differ from uniformity on a set of positive measure.

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arXiv2026

Multivariate lattice deformation: A spatially explicit framework for assessing crop rotation impacts on soil nutrient dynamics

Crop rotation impacts on soil nutrients are typically assessed using field-averaged or single-nutrient analyses that ignore spatial heterogeneity and multivariate interactions. We propose a multivariate lattice model treating soil as a 4D tensor (space, time, and N, P, K channels). Crop rotations are represented as force vectors, with soil buffering capacity ("stiffness") varying spatially with texture. Lateral nutrient movement is introduced via kernel smoothing. Cumulative impact is quantified by Euclidean distance in N-P-K space, with significance assessed via Cramer-von Mises permutation tests. Simulating a three-year corn-soybean-wheat rotation on a 20 x 20 heterogeneous grid shows mean stress of 0.63 after one cycle, with maximum 0.91 in sandy areas. Phosphorus depletion (17.9%) exceeds nitrogen (10.8%), dominating stress in 19% of cells - obscured by single-nutrient analyses. Continuous corn increases mean stress by 41%. Cramer-von Mises tests detect significant deviation (p <= 0.002), and Moran's I (0.29-0.30) confirms spatial autocorrelation. Our framework identifies risk zones and guides site-specific management, bridging geostatistics with mechanistic crop models.

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arXiv2026

Detecting Distributional Differences in Spatially Correlated Multivariate Data via Kernel-Smoothed Rank-Based Empirical Copula Tests

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.

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arXiv2024

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

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 $\alpha$-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.

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