| Abstract: | Due to the irregularity of finite mixture models, the commonly used likelihood-ratio statistics often have complicated limiting distributions. We propose to add a particular type of penalty function to the log-likelihood function. The resulting penalized likelihood-ratio statistics have simple limiting distributions when applied to finite mixture models with multinomial observations. The method is especially effective in addressing the problems discussed by Chernoff and Lander (1995). The theory developed and simulations conducted show that the penalized likelihood method can give very good results, better than the well-known C(α) procedure, for example. The paper does not, however, fully explore the choice of penalty function and weight. The full potential of the new procedure is to be explored in the future. |
