mixqr: An Extensible Framework for Mixtures of Quantile and Expectile Regressions

An extensible expectation-maximization (EM) framework for finite mixtures of quantile regressions (clusterwise / mixture-of-experts quantile regression). A single EM substrate with an engine/extension contract carries a family of capabilities: the core free-weight mixture of Wu and Yao (2016) – a fast asymmetric-Laplace path and the nonparametric kernel-density EM with components constrained to have their tau-quantile equal to zero; expectile and M-quantile component-loss families; component-specific penalized variable selection; and joint multi-quantile estimation with a shared classification and non-crossing curves. The companion package mixqrgate adds location-varying gating.

Main entry points

• mixqr() – fit a mixture of quantile (or, via family=, expectile / M-quantile) regressions.

• mixqr_pen() – component-specific penalized variable selection.

• mixqr_nc() – joint multi-quantile estimation with non-crossing.

• mixqr_select() – choose the number of components by AIC/BIC.

• sim_mixqr2(), sim_mixqr3() – Wu & Yao simulation designs.

• register_mixqr_engine() – register a custom EM engine (the extension contract on which the capabilities are built).

References

Wu, Q. and Yao, W. (2016). Mixtures of quantile regressions. Computational Statistics & Data Analysis 93, 162–176.

Hall, P. and Presnell, B. (1999). Density estimation under constraints. Journal of Computational and Graphical Statistics 8, 259–277.

Koenker, R. and Bassett, G. (1978). Regression quantiles. Econometrica 46, 33–50.

See also

Useful links:

• https://github.com/kvenkita/mixqr

• https://kvenkita.github.io/mixqr/

• Report bugs at https://github.com/kvenkita/mixqr/issues

Author

Maintainer: Kailas Venkitasubramanian kailasv@gmail.com [copyright holder]