On the Exponential Approximation of Type II Error Probability of Distributed Test of Independence

This paper studies distributed binary test of statistical independence under communication (information bits) constraints. While testing is very relevant in various applications, particularly useful for event detection sensor networks where data correlation often occurs among observations devices the presence a signal interest. By focusing on case two because their tractability, we begin by investigating conditions Type I error probability restrictions which minimum II admits an exponential behavior with sample size. Then, study finite sample-size regime this problem. We derive new upper and lower bounds gap between its approximation different setups, including imposed vanishing probability. Our theoretical results shed light regimes at approximations via exponents became informative enough sense predicting well actual finally discuss application our evaluated numerically, show that are not only tractable but also valuable proxy finite-length regime.