Partial likelihood for real-time signal processing

We introduce a unified statistical framework for real-time signal processing with neural networks by using a recent extension of maximum likelihood (ML) estimation, partial likelihood (PL) estimation theory, which allows for (i) dependent observations, and (ii) processing of data using only the information that is available at the time of processing. For a general neural network conditional distribution model, we establish a fundamental information-theoretic relationship for PL estimation, and obtain large sample properties of PL for the general case of dependent observations. We consider applications of PL to prediction and channel equalization.