Accelerating the pool-adjacent-violators algorithm for isotonic distributional regression

TL;DR

This paper presents an improved version of the pool-adjacent-violators algorithm (PAVA) that significantly reduces computation time for estimating stochastically ordered distribution functions by analyzing the dependence of weighted least squares fits.

Contribution

The paper introduces a novel modification to PAVA that accelerates its performance in isotonic distributional regression tasks.

Findings

Reduced computation times for PAVA in distributional regression

Enhanced understanding of weighted least squares dependence

Potential for broader application in stochastic ordering problems

Abstract

In the context of estimating stochastically ordered distribution functions, the pool-adjacent-violators algorithm (PAVA) can be modified such that the computation times are reduced substantially. This is achieved by studying the dependence of antitonic weighted least squares fits on the response vector to be approximated.