Universal Inference Meets Random Projections: A Scalable Test for Log-concavity

• URL: http://arxiv.org/abs/2111.09254v4
• Date: Mon, 15 Apr 2024 02:37:16 GMT
• Title: Universal Inference Meets Random Projections: A Scalable Test for Log-concavity
• Authors: Robin Dunn, Aditya Gangrade, Larry Wasserman, Aaditya Ramdas,
• Abstract summary: We present the first test of log-concavity that is provably valid in finite samples in any dimension. We find that a random projections approach that converts the d-dimensional testing problem into many one-dimensional problems can yield high power.
• Score: 30.073886309373226
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Shape constraints yield flexible middle grounds between fully nonparametric and fully parametric approaches to modeling distributions of data. The specific assumption of log-concavity is motivated by applications across economics, survival modeling, and reliability theory. However, there do not currently exist valid tests for whether the underlying density of given data is log-concave. The recent universal inference methodology provides a valid test. The universal test relies on maximum likelihood estimation (MLE), and efficient methods already exist for finding the log-concave MLE. This yields the first test of log-concavity that is provably valid in finite samples in any dimension, for which we also establish asymptotic consistency results. Empirically, we find that a random projections approach that converts the d-dimensional testing problem into many one-dimensional problems can yield high power, leading to a simple procedure that is statistically and computationally efficient.

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