RT info:eu-repo/semantics/article
T1 Robust estimation of mixtures of regressions with random covariates, via trimming and constraints
A1 García Escudero, Luis Ángel
A1 Gordaliza Ramos, Alfonso
A1 Greselin, Francesca
A1 Ingrassia, Salvatore
A1 Mayo Iscar, Agustín
K1 Análisis multivariante
AB A robust estimator for a wide family of mixtures of linear regression is presented.Robustness is based on the joint adoption of the Cluster Weighted Model andof an estimator based on trimming and restrictions. The selected model provides theconditional distribution of the response for each group, as in mixtures of regression,and further supplies local distributions for the explanatory variables. A novel versionof the restrictions has been devised, under this model, for separately controlling thetwo sources of variability identified in it. This proposal avoids singularities in thelog-likelihood, caused by approximate local collinearity in the explanatory variablesor local exact fits in regressions, and reduces the occurrence of spurious local maximizers.In a natural way, due to the interaction between the model and the estimator,the procedure is able to resist the harmful influence of bad leverage points along theestimation of the mixture of regressions, which is still an open issue in the literature.The given methodology defines a well-posed statistical problem, whose estimator existsand is consistent to the corresponding solution of the population optimum, underwidely general conditions. A feasible EM algorithm has also been provided to obtainthe corresponding estimation. Many simulated examples and two real datasets havebeen chosen to show the ability of the procedure, on the one hand, to detect anomalousdata, and, on the other hand, to identify the real cluster regressions without theinfluence of contamination.Keywords Cluster Weighted Modeling · Mixture of Regressions · Robustness
PB Universidad de Valladolid. Facultad de Medicina
YR 2015
FD 2015
LK http://uvadoc.uva.es/handle/10324/11617
UL http://uvadoc.uva.es/handle/10324/11617
LA eng
NO Arxiv, Febrero 2015, vol.1, p.1-30
NO Producción Científica
DS UVaDOC
RD 24-nov-2024