The Minimum Phone Error (MPE) criterion for discriminative training was shown to be able to offer acoustic models with significantly improved performance. This concept was then further extended to Feature-space Minimum Phone Error (fMPE) and offset fMPE for training feature parameters as well. This paper reviews the concept of MPE and reports the experiments and results in performing MPE, fMPE and offset fMPE on the task of Mandarin Broadcast News, and significant improvements were obtained similar to the results reported for other languages and other tasks by other sites. In addition, a new concept of dimension-weighted offset fMPE is proposed in this work and even better performance than offset fMPE was obtained.