A computational strategy for doubly smoothed MLE exemplified in the normal mixture model
A typical problem for the parameter estimation in normal mixture models is an unbounded likelihood and the presence of many spurious local maxima. To resolve this problem, we apply the doubly smoothed maximum likelihood estimator (DS-MLE) proposed byÂ Seo and Lindsay (inÂ preparation). We discuss the computational issues of the DS-MLE and propose a simulation-based DS-MLE using Monte Carlo methods as a general computational tool. Simulation results show that the DS-MLE is virtually consistent for any bandwidth choice. Moreover, the parameter estimates in the DS-MLE are quite robust to the choice of bandwidths, as the theory indicates. A new method for the bandwidth selection is also proposed.
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- Gabriela Ciuperca & Andrea Ridolfi & Jérome Idier, 2003. "Penalized Maximum Likelihood Estimator for Normal Mixtures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 45-59.
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- Chen, Jiahua & Tan, Xianming, 2009. "Inference for multivariate normal mixtures," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1367-1383, August.
- Hall, Peter, 1990. "Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 177-203, February.
- Ingrassia, Salvatore & Rocci, Roberto, 2007. "Constrained monotone EM algorithms for finite mixture of multivariate Gaussians," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5339-5351, July.
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