Kernel-Based Nonparametric Tests For Shape Constraints

• URL: http://arxiv.org/abs/2510.16745v2
• Date: Tue, 21 Oct 2025 01:05:47 GMT
• Title: Kernel-Based Nonparametric Tests For Shape Constraints
• Authors: Rohan Sen,
• Abstract summary: We derive statistical properties of the sample estimator and provide rigorous theoretical guarantees.<n>We introduce a joint Wald-type statistic to test for shape constraints over finite grids.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a reproducing kernel Hilbert space (RKHS) framework for nonparametric mean-variance optimization and inference on shape constraints of the optimal rule. We derive statistical properties of the sample estimator and provide rigorous theoretical guarantees, such as asymptotic consistency, a functional central limit theorem, and a finite-sample deviation bound that matches the Monte Carlo rate up to regularization. Building on these findings, we introduce a joint Wald-type statistic to test for shape constraints over finite grids. The approach comes with an efficient computational procedure based on a pivoted Cholesky factorization, facilitating scalability to large datasets. Empirical tests suggest favorably of the proposed methodology.

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