In this paper, we extend the Maximum Likelihood (ML) training algorithm to the Minimum classification error (MCE) training algorithm for optimal estimation of the state-dependent polynomial coefficients in the trended HMM [2]. The problem of automatic speech recognition is viewed as a discriminative dynamic data-fitting problem, where nl- otiue (not absolute) closeness in fitting an array of dynamic speech models to the unknown speech data sequence provides the recognition decision. In this view, the properties of the MCE formulation for training the trended HMM are analyzed by fitting raw speech data using MCE-trained trended BMMS, contrasting the poor discriminative fitting using the MCE-trained models. Comparisons between the phonetic classification as well as data-fitting results obtained with ML and -114th MCE training algorithms demonstrate the effectiveness of the discriminatively trained trended HMMs.