Semi-parametric mixtures of quantile regressions

Abstract

Mixtures of quantile regressions are explored through the lens of a kernel density based EM-type algorithm and a newly proposed CEM-type algorithm. This allows the simultaneous clustering and modeling of conditional quantiles without the need to assume symmetric or identical error distributions for any of the components. We conduct simulation studies and apply both algorithms to real life datasets. The first has already been investigated by fitting the EM-type algorithm and we show that the CEM-type algorithm produces similar results. The second is a homoscedastic dataset which has been explored through the lens of univariate quantile regression. We begin by modeling the mixtures of the conditional medians as a robust alternative to mixtures of conditional means. Mixtures of other conditional quantiles are modeled as well to get a more complete understanding of the conditional distribution. This, however, proves to be a challenging task for datasets which are not easily separable and may lead to unsatisfactory results, especially when considering low quantiles or high quantiles such as 0.1 or 0.9 respectively. The theory of the EM-type algorithm is provided in detail and the proposed CEM-type algorithm is shown to provide a substantial improvement in the model convergence speed, but often at the cost of increased bias in the parameter estimates. We conclude with a discussion of some of the limitations and areas for future research.