A method and apparatus are disclosed for training a pattern recognition system, such as a speech recognition system, using an improved objective function. The concept of rank likelihood, previously applied only to the decding process, is applied in a novel manner to the parameter estimation of the training phase of a pattern recognition system. The disclosed objective function is based on a pseudo-rank likelihood that not only maximizes the likelihood of an observation for the correct class, but also minimizes the likelihoods of the observation for all other classes, such that the discrimination between classes is maximized. A training process is disclosed that utilizes the pseudo-rank likelihood objective function to identify model parameters that will result in a pattern recognizer with the lowest possible recognition error rate. The discrete nature of the rank-based rank likelihood objective function is transformed to allow the parameter estimations to be optimized during the training phase.