Douglas Landsittel | Searcharxiv

arXiv2026

A Relativity-Based Framework for Statistical Testing Guided by the Independence of Ancillary Statistics: Methodology and Nonparametric Illustrations

This paper introduces a decision-theoretic framework for constructing and evaluating test statistics based on their relationship with ancillary statistics-quantities whose distributions remain fixed under the null and alternative hypotheses. Rather than focusing solely on maximizing discriminatory power, the proposed approach emphasizes reducing dependence between a test statistic and relevant ancillary structures. We show that minimizing such dependence can yield most powerful (MP) procedures. A Basu-type independence result is established, and we demonstrate that certain MP statistics also characterize the underlying data distribution. The methodology is illustrated through modifications of classical nonparametric tests, including the Shapiro-Wilk, Anderson-Darling, and Kolmogorov-Smirnov tests, as well as a test for the center of symmetry. Simulation studies highlight the power and robustness of the proposed procedures. The framework is computationally simple and offers a principled strategy for improving statistical testing.

stat.ME↗

arXiv2026

Measuring Neural Network Complexity via Effective Degrees of Freedom

Quantifying the complexity of feed-forward neural networks (FFNNs) remains challenging due to their nonlinear, hierarchical structure and numerous parameters. We apply generalized degrees of freedom (GDF) to measure model complexity in FFNNs with binary outcomes, adapting the algorithm for discrete responses. We compare GDF with both the effective number of parameters derived via log-likelihood cross-validation and the null degrees of freedom of Landsittel et al. Through simulation studies and a real data analysis, we demonstrate that GDF provides a robust assessment of model complexity for neural network models, as it depends only on the sensitivity of fitted values to perturbations in the observed responses rather than on assumptions about the likelihood. In contrast, cross-validation-based estimates of model complexity and the null degrees of freedom rely on the correctness of the assumed likelihood and may exhibit substantial variability. We find that GDF, cross-validation-based measures, and null degrees of freedom yield similar assessments of model complexity only when the fitted model adequately represents the data-generating mechanism. These findings highlight GDF as a stable and broadly applicable measure of model complexity for neural networks in statistical modeling.

stat.ME↗