Nearly Optimum Properties of Certain Multi-Decision Sequential Rules for General Non-i.i.d. Stochastic Models

2024/05/02 by Alexander G. Tartakovsky, Tartakovsky, Alexander G. · 1 citation
Computer Science · #62G40 #62L10 #62L15 #Bayesian Modeling and Causal Inference #FOS: Mathematics #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2405.00928

openalex publication_date 2024/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Dedicated to the memory of Professor Tze Leung Lai, this paper introduces three multi-hypothesis sequential tests. These tests are derived from one-sided versions of the sequential probability ratio test and its modifications. They are proven to be first-order asymptotically optimal for testing simple and parametric composite hypotheses when error probabilities are small. These tests exhibit near optimality properties not only in classical i.i.d. observation models but also in general non-i.i.d. models, provided that the log-likelihood ratios between hypotheses converge r-completely to positive and finite numbers. These findings extend the seminal work of Lai (1981) on two hypotheses.

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• Change, dependence, and discovery: Celebrating the work of T.L. Lai

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