Locally most powerful sequential tests of a simple hypothesis vs. One-sided alternatives for independent observations

TL;DR

This paper characterizes the structure of the most powerful sequential tests for testing a simple hypothesis against one-sided alternatives in a process with independent observations, focusing on local optimality in the Berk sense.

Contribution

It provides a theoretical characterization of the structure of locally most powerful sequential tests for simple vs. one-sided hypotheses with independent data.

Findings

Identifies the form of optimal sequential tests under local alternatives

Provides conditions for the existence of such tests

Enhances understanding of sequential testing in parametric models

Abstract

Let $X_1,X_2,..., X_n,...$ be a stochastic process with independent values whose distribution $P_\theta$ depends on an unknown parameter $\theta$, $\theta\in\Theta$, where $\Theta$ is an open subset of the real line. The problem of testing $H_0:$ $\theta=\theta_0$ vs. a composite alternative $H_1:$ $\theta>\theta_0$ is considered, where $\theta_0\in\Theta$ is a fixed value of the parameter. The main objective of this work is the characterization of the structure of the locally most powerful (in the sense of Berk) sequential tests in this problem.