B0524
Title: Quantile ratio regression
Authors: Marco Geraci - Sapienza University of Rome (Italy) [presenting]
Alessio Farcomeni - University of Rome Tor Vergata (Italy)
Abstract: Quantile ratio regression is introduced. The proposed model assumes that the ratio of two arbitrary quantiles of a continuous response distribution is a function of a linear predictor. For estimation, an iterative, two-step algorithm is developed whereby, at each step, a regression problem is solved for one quantile at a time, conditional on the other quantile. Thanks to basic quantile properties, the algorithm can be carried out on the scale of either the response or the link function. The advantage of using the latter becomes tangible when implementing fast optimisers for linear regression in the presence of large datasets. The theoretical properties of the estimator are shown and an efficient method is derived to obtain standard errors. The good performance and merit of the methods are illustrated by means of a simulation study. In a real data analysis, income inequality is investigated in the European Union (EU) using data from a sample of about two million households. A significant association between inequality is found, as measured by quantile ratios, and certain macroeconomic indicators, and countries with outlying inequality relative to the rest of the EU are identified. An R implementation of the proposed methods is available.
