Order Selection in Finite Mixture Models With a Nonsmooth Penalty
提出一种改进的平滑剪裁绝对偏差（MSCAD）惩罚似然方法，用于有限混合模型的阶数选择，通过引入两个依赖混合比例和分量参数的惩罚函数，在估计模型阶数和混合分布上具有一致性，模拟和实例表明其优于AIC、BIC等方法。
AbstractOrder selection is a fundamental and challenging problem in the application of finite mixture models. In this article, we develop a new penalized likelihood approach. The new method, modified smoothly clipped absolute deviation (MSCAD), deviates from information-based methods such as Akaike information criterion (AIC) and Bayesian information criterion (BIC) by introducing two penalty functions that depend on the mixing proportions and the component parameters. It is consistent at estimating both the order of the mixture model and the mixing distribution. Simulations show that MSCAD has much better performance than a number of existing methods. Two real-data examples are examined to illustrate the performance of MSCAD.KEY WORDS: Expectation-maximization (EM) algorithmFinite mixture modelPenalty methodSmoothly clipped absolute deviation (SCAD)