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This article is concerned with decentralized sequential testing of a normalmean $\mu$ with two-sided alternatives. It is assumed that in a single-sensornetwork system with limited local memory, i.i.d. normal raw observations areobserved at the local sensor, and quantized into binary messages that are sentto the fusion center, which makes a final decision between the null hypothesis$H_0: \mu = 0$ and the alternative hypothesis $H_1: \mu = \pm 1.$ We propose adecentralized sequential test using the idea of tandem quantizers (orequivalently, a one-shot feedback). Surprisingly, our proposed test only usesthe quantizers of the form $I(X_{n} \ge \lambda),$ but it is shown to beasymptotically Bayes. Moreover, by adopting the principle of invariance, wealso investigate decentralized invariant tests with the stationary quantizersof the form $I(|X_{n}| > \lambda),$ and show that $\lambda = 0.5$ only leads toa suboptimal decentralized invariant sequential test. Numerical simulations areconducted to support our arguments.

Decentralized Two-Sided Sequential Tests for A Normal Mean