Conditional mid-quantiles: modelling, estimation and applications

Abstract

In the continuous case, the quantile function is defined as the inverse of the cumulative distribution function (CDF). The asymptotic properties of sample quantiles, including normality, have been established in a variety of settings. In the discrete case, quantiles are not unique, and inference becomes troublesome. A possible way out is offered by mid-quantiles. These are obtained by inverting the mid-CDF, which is closely related to Lancaster’s mid-p-value. Mid-quantiles, which can be seen as a bridge between quantiles of continuous and discrete distributions, provide not only advantages for inference in general but also a sensible interpretation when the distribution is discrete. In this talk, I will introduce regression methods for conditional mid-quantiles (Stat Med Res, 31(5), 2022), along with recent applications to longitudinal data analysis (J Stat Comput Simul, 94(12), 2024) and graphical modelling (arXiv:2309.05084v2).