Quickest Change Detection with Leave-one-out Density Estimation

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Abstract

The problem of quickest change detection in a sequence of independent observations is considered. The pre-change distribution is assumed to be known, while the post-change distribution is completely unknown. A window-limited leave-one-out (LOO) CuSum test is developed, which does not assume any knowledge of the post-change distribution, and does not require any post-change training samples. It is shown that, with certain convergence conditions on the density estimator, the LOO-CuSum test is first-order asymptotically optimal, as the false alarm rate goes to zero. The analysis is validated through numerical results, where the LOO-CuSum test is compared with baseline tests that have distributional knowledge.

Keywords

  • (kernel) density estimation
  • Quickest change detection (QCD)
  • non-parametric statistics

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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