Universal Inference Meets Random Projections: A Scalable Test for Log-concavity
Journal of Computational and Graphical Statistics(2021)
摘要
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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