Tag Archives: expectile

Quantile and Expectile Regression for random effects model

Our joint paper with Amadou Diogo Barry and Karim Oualkacha is now available on https://hal.archives-ouvertes.fr/hal-01421752

Quantile and expectile regression models pertain to the estimation of unknown quantiles/expectiles of the cumulative distribution function of a dependent variable as a function of a set of covariates and a vector of regression coefficients. Both approaches make no assumption on the shape of the distribution of the response variable, allowing for investigation of a comprehensive class of covariate effects. This paper fits both quantile and expectile regression models within a random effects framework for dependent/panel data. It provides asymptotic properties of the underlying model parameter estimators and suggests appropriate estimators of their variances-covariances matrices. The performance of the proposed estimators is evaluated through exhaustive simulation studies and the proposed methodology is illustrated using real data. The simulation results show that expectile regression is comparable to quantile regression, easily computable and has relevant statistical properties. In conclusion, expectiles are to the mean what quantiles are to the median, and they should be used and interpreted as quantilized mean.

https://freakonometrics.hypotheses.org/files/2016/11/exp-quant-reg-1.png

Quantile and Expectile Regressions

Tomorrow afternoon, because Pavel Shevchenko is currently in Rennes, there will be a small workshop. I will present some recent work with Amadou Barry and Karim Oualkacha on quantile and expectile regressions (our work is more specifically on panel regressions, with random effect models, quantile QRRE and expectile ERRE) but tomorrow, it will be more an introduction.  Slides are available online.