Mid-quantile regression for discrete outcomes

Relatore

Alessio Farcomeni – University of Rome Tor Vergata

Abstract
We develop quantile regression methods for discrete responses by extending Parzen's definition of marginal mid-quantiles. We thus define a conditional mid-distribution function. After interpolation, we define the conditional mid-quantile function as its inverse. We propose a two-step estimator whereby, in the first step, conditional mid-probabilities are obtained non-parametrically and, in the second step, regression coefficients are estimated by solving an implicit equation. When constraining the quantile index to a data-driven admissible range, the second-step estimating equation has a least-squares type, closed-form solution. The proposed estimator is shown to be strongly consistent and asymptotically normal under general conditions. A simulation study and real data applications are presented. Our methods can be applied to a large variety of discrete responses, including binary, ordinal, and count variables.
An implementation of our approach can be found in the R library Qtools, freely available on CRAN.

Organizzatore

Cinzia Viroli