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

TL;DR

This paper introduces an almost-fixed-length hypothesis testing method that nearly guarantees fixed sample size decisions while allowing rare additional sampling, enhancing the trade-off between error exponents compared to classical methods.

Contribution

It characterizes the error exponents for this new testing class, bridging fixed-sample and sequential testing, and improves error trade-offs.

Findings

Characterized maximum error exponents for the new test class.

Showed the test bridges fixed-sample and sequential testing.

Demonstrated improved error trade-offs over classical methods.

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.