Robust mixture modeling based on two-piece scale mixtures of normal family. (English) Zbl 1432.62029
Summary: In this paper, we examine the finite mixture (FM) model with a flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family components. This family allows the development of a robust estimation of FM models. The TP-SMN is a rich class of distributions that covers symmetric/asymmetric and light/heavy tailed distributions. It represents an alternative family to the well-known scale mixtures of the skew normal (SMSN) family studied by M. D. Branco and D. K. Dey [J. Multivariate Anal. 79, No. 1, 99–113 (2001; Zbl 0992.62047)]. Also, the TP-SMN covers the SMN (normal, t, slash, and contaminated normal distributions) as the symmetric members and two-piece versions of them as asymmetric members. A key feature of this study is using a suitable hierarchical representation of the family to obtain maximum likelihood estimates of model parameters via an EM-type algorithm. The performances of the proposed robust model are demonstrated using simulated and real data, and then compared to other finite mixture of SMSN models.
MSC:
| 62E10 | Characterization and structure theory of statistical distributions |
| 62H10 | Multivariate distribution of statistics |
Keywords:
ECME algorithm; finite mixture model; maximum likelihood estimates; scale mixtures of normal family; two-piece distributionsCitations:
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