Detectors for multinomial input

The binary detection problem is considered. Under an arbitrary noise environment, the input sample space can be transformed into a multinominal 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 chi-square statistic. The resulting detectors are compared to others in terms of asymptotic relative efficiency under some actual noise distributions.