Laplace mixture of linear experts

Mixture of Linear Experts (MoLE) models provide a popular framework for modeling nonlinear regression data. The majority of applications of MoLE models utilizes a Gaussian distribution for regression error. Such assumptions are known to be sensitive to outliers. The use of a Laplace distributed error is investigated. This model is named the Laplace MoLE (LMoLE). Links are drawn between the Laplace error model and the least absolute deviations regression criterion, which is known to be robust among a wide class of criteria. Through application of the minorization–maximization algorithm framework, an algorithm is derived that monotonically increases the likelihood in the estimation of the LMoLE model parameters. It is proven that the maximum likelihood estimator (MLE) for the parameter vector of the LMoLE is consistent. Through simulation studies, the robustness of the LMoLE model over the Gaussian MOLE model is demonstrated, and support for the consistency of the MLE is provided. An application of the LMoLE model to the analysis of a climate science data set is described.