Reliability of Sequential Hypothesis Testing Can Be Achieved by an Almost-Fixed-Length Test

Anusha Lalitha; Tara Javidi

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arXiv · 1605.04851

Reliability of Sequential Hypothesis Testing Can Be Achieved by an Almost-Fixed-Length Test

Anusha Lalitha·Tara Javidi

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Abstract

The maximum type-I and type-II error exponents associated with the newly introduced almost-fixed-length hypothesis testing is characterized. In this class of tests, the decision-maker declares the true hypothesis almost always after collecting a fixed number of samples $n$; however in very rare cases with exponentially small probability the decision maker is allowed to collect another set of samples (no more than polynomial in $n$). This class of hypothesis tests are shown to bridge the gap between the classical hypothesis testing with a fixed sample size and the sequential hypothesis testing, and improve the trade-off between type-I and type-II error exponents.

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Anusha Lalitha, Tara Javidi. 2016-05-17. Reliability of Sequential Hypothesis Testing Can Be Achieved by an Almost-Fixed-Length Test. https://arxiv.org/abs/1605.04851

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