An asymptotically least-favorable Chernoff bound for a large class of dependent data processes

Abstract

It is desired to determine the worst-case asymptotic error probability performance of a given detector operating in an environment of uncertain data dependency. A class of Markov data process distributions is considered which satisfy a one-shift dependency bound and agree with a specified univariate distribution. Within this dependency contamination class the distribution structure which minimizes the exponential rate of decrease of detection error probabilities is identified. This is a uniform least-favorability principle, because the least-favorable dependency structure is the same for all bounded memoryless detectors. The error probability exponential rate criterion used is a device of large deviations theory. The results agree well with previous results obtained using Pitman's asymptotic relative efficiency (ARE), which is a more tractable small-signal performance criterion. In contrast to ARE, large deviations theory is closely related to finite-sample error probabilities via the finite-sample Chernoff bounds and other exponentially tight bounds and other approximations.