|Title: ||Robust estimation of mixtures of regressions with random covariates, via trimming and constraints|
|Authors: ||García Escudero, L. A.|
Gordaliza Ramos, Alfonso
Mayo Iscar, Agustín
|Issue Date: ||2015|
|Publisher: ||Universidad de Valladolid. Facultad de Medicina|
|Description: ||Producción Científica|
|Citation: ||Arxiv, Febrero 2015, vol.1, p.1-30|
|Abstract: ||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 and
of an estimator based on trimming and restrictions. The selected model provides the
conditional distribution of the response for each group, as in mixtures of regression,
and further supplies local distributions for the explanatory variables. A novel version
of the restrictions has been devised, under this model, for separately controlling the
two sources of variability identified in it. This proposal avoids singularities in the
log-likelihood, caused by approximate local collinearity in the explanatory variables
or 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 the
estimation 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 exists
and is consistent to the corresponding solution of the population optimum, under
widely general conditions. A feasible EM algorithm has also been provided to obtain
the corresponding estimation. Many simulated examples and two real datasets have
been chosen to show the ability of the procedure, on the one hand, to detect anomalous
data, and, on the other hand, to identify the real cluster regressions without the
influence of contamination.
Keywords Cluster Weighted Modeling · Mixture of Regressions · Robustness|
|Keywords: ||Análisis multivariante|
|Peer Review: ||SI|
|Appears in Collections:||DEP24 - Artículos de revista|