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Abstract:
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The problem of detecting and isolating the underlying correlation structure in a number of Gaussian information sources is considered using sequentially acquired observations. It is assumed that an observation is obtained from each source at each sampling time and the observations are independent over time. The goal is to stop sampling as quickly as possible and to declare upon stopping whether there is at least one correlated pair or not, and if yes, to identify all the correlated pairs with strong correlation. Specifically, it is required to control explicitly the error probabilities of three kinds: false alarm when all the sources are independent, and family wise type I and type II errors when a correlation structure is present. We propose a procedure that not only controls explicitly these three error metrics but also achieves the smallest possible average sample size, to a first-order approximation, as the target error rates go to 0. Finally, a simulation study is presented that describes the performance of the proposed procedure in terms of the average sample size and performs better while compared to the alternative testing procedures.
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