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To minimize the expected total sampling cost in sequential testing about a random vector

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  • Xing, Yiming

Abstract

This paper considers the problem of testing multiple hypotheses about the distribution of a random vector based on sequentially sampled observations from it. It is assumed that sampling from a different subset of dimensions incurs a different cost, and the goal is to minimize the expected total sampling cost while controlling the probabilities of misidentifying the true hypothesis below user-specified levels. The proposed testing procedure is shown to achieve this goal asymptotically as the levels go to zero. Specifically, it works by greedily following the optimal sampling distribution based on the current maximum likelihood hypothesis while guaranteeing sufficient exploration of all dimensions, and selecting the maximum likelihood hypothesis when the likelihood for it exceeds the likelihoods for all other hypotheses by sufficient margins. Numerical studies in the multivariate Gaussian case are presented for illustration.

Suggested Citation

  • Xing, Yiming, 2026. "To minimize the expected total sampling cost in sequential testing about a random vector," Journal of Multivariate Analysis, Elsevier, vol. 215(C).
    • Handle: RePEc:eee:jmvana:v:215:y:2026:i:c:s0047259x26000461
    DOI: 10.1016/j.jmva.2026.105640
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