| Abstract: | Finite mixture models have wide applications in practice. However, due to the irregularity of its parameter sauce, bony commonly ed statistical methods do not have theoretical backups in the finite future duel context. It regains unknown, for example, whether the maximum likelihoodestimetor of the mixing distribution achieves the optimal convergence rate n-1/4 which is already unusually low. In mis peper, we study a Class of restricted restricted maximum likelihood estimetors. It is shown that the estimator we propose achieves the optimal rate. In addition, we show that in the model where a structural parameter is involved, the convergence rate for estimetins the structural parameter is the usual n-1/2, not affected by the difficulties in estimetins the mixing distribution. Limiting distributions of some functionals of the rotried maximum likelitiwt estimetors are discussed. |
