Detectors for Multiomial Input

The binary detection problem is considered. Under an arbitrary noise environment, the input sample space can be transformed into a multinomial vector. Based on observations of this vector, the Neyman-Pearson optimal detector is developed for a known signal. When the signal strength is unknown, the likelihood ratio principle is followed to obtain consistent tests which use the Pearson's chisquare statistic. The resulting detectors are compared to others in terms of asymptotic relative efficiency under some actual noise distributions.