This dissertation develops basic theory and applications of statistical multirate signal processing. Specific tools and terminology for describing multirate systems in the time and frequency domains are presented. An optimal multirate estimator is derived in both a direct form and recursive form. The Recursive form of the optimal estimator allows calculation of the relative change in performance when input signals are added or removed from the multirate system. The optimal multirate filtering problem also is specialized to the case of optimal multirate linear prediction. An efficient method for calculating the multirate linear prediction coefficients and error variances is developed through the use of the multichannel Levinson recursion and generalized triangular UL factorization. Finally, a multirate sequential classifier is derived and applied to the problem of target classification. It is shown that classifier parameters needed for implementing the multirate sequential classifier are the same as those for multirate linear prediction. The methods presented in this dissertation are useful for multisensor fusion particularly when the sensors are operating at different rates.