AI & ML
Maximal Inequalities for Empirical Processes under General Mixing Conditions
arXiv stat.TH0 views
arXiv:2402.11394v5 Announce Type: replace-cross Abstract: This paper provides a bound for the supremum of sample averages over a class of functions for a general class of mixing stochastic processes with arbitrary mixing rates. Regardless of the speed of mixing, the bound is comprised of a concentration rate and a novel measure of complexity. The speed of mixing, however, affects the former quantity implying a phase transition. Fast mixing leads to the standard root-n concentration rate, while slow mixing leads to a slower concentration rate whose speed depends on the mixing structure. Our findings are applied to obtain new Glivenko-Cantelli type results.
Source：https://arxiv.org/abs/2402.11394PreviousThe Geometry of Latent Spaces: Projective Invariants, Structural Identification, and Ratio-Scale MeasurementNextNon-Gaussian Uncertainty Estimation via Semi-nonparametric Density
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