A discriminant function-based minimum recognition error rate pattern recognition approach is described and studied for various applications in speech processing. This approach departs from the conventional paradigm, which links a classification/recognition task to the problem of distribution estimation. Instead, it takes a discriminant function based statistical pattern recognition approach. The suitability of this approach for classification error rate minimization is established through a special loss function. It is meaningful even when the model correctness assumption is known to be not valid. We study the theoretical basis of this approach and compare it with various criteria used in speech recognition. We differentiate the method of classifier design by way of distribution estimation and the discriminant function methods of minimizing classification error rate, based on the fact that in many realistic applications, such as speech recognition, the true distribution form of the source is rarely known precisely, and without model correctness assumption, the classical optimality theory of the distribution estimation approach cannot be applied directly. We discuss issues in this new classifier design paradigm and present various extensions of this approach to classifier design applications in speech processing.