Smoothed quantile regression processes for binary response models

TL;DR

This paper develops a novel approach using smoothed quantile regression processes to estimate binary response models, avoiding restrictive assumptions and providing new asymptotic results.

Contribution

It introduces a unified framework for binary response models based on quantile processes, generalizing previous methods and eliminating the need for specific link functions.

Findings

Derived a uniform linearisation for the empirical quantile process

Established asymptotic normality of the estimators

Showed effectiveness in estimating binary choice probabilities

Abstract

In this paper, we consider binary response models with linear quantile restrictions. Considerably generalizing previous research on this topic, our analysis focuses on an infinite collection of quantile estimators. We derive a uniform linearisation for the properly standardized empirical quantile process and discover some surprising differences with the setting of continuously observed responses. Moreover, we show that considering quantile processes provides an effective way of estimating binary choice probabilities without restrictive assumptions on the form of the link function, heteroskedasticity or the need for high dimensional non-parametric smoothing necessary for approaches available so far. A uniform linear representation and results on asymptotic normality are provided, and the connection to rearrangements is discussed.