Quantization for distributed testing of independence

We consider the problem of distributed test of statistical independence under communication constraints. While independence test is frequently encountered in various applications, distributed independence test is particularly useful for events detection in sensor networks: data correlation often occurs among sensor observations in the presence of a target. Focusing on the Gaussian case because of its tractability, we study in this paper the characteristics of optimal scalar quantizers for distributed test of independence where the optimality is in the sense of optimizing the error exponent. We also discuss the optimal quantizer properties for the finite sample regime, i.e., that of directly minimizing the error probability.