Universal Inference Meets Random Projections: A Scalable Test for Log-Concavity
本文提出首个在任意维度有限样本下有效且渐近一致的对数凹性检验，利用随机投影将高维问题转化为多个一维问题，提升检验功效和计算效率，适用于经济学、生存分析和可靠性理论。
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.