Certainty bands for the conditional cumulative distribution function and applications

TL;DR

This paper develops uniform asymptotic certainty bands for the conditional cumulative distribution function, providing precise consistency rates for local linear estimators, with applications demonstrated through simulations and real data analysis.

Contribution

It introduces the first uniform asymptotic certainty bands for the conditional CDF and establishes exact consistency rates for local linear estimators.

Findings

Exact rate of strong uniform consistency for local linear estimator

Asymptotic certainty bands for quantiles and regression functions

Validated results with simulations and real data application

Abstract

In this paper, we establish uniform asymptotic certainty bands for the conditional cumulative distribution function. To this aim, we give exact rate of strong uniform consistency for the local linear estimator of this function. The corollaries of this result are the asymptotic certainty bands for the quantiles and the regression function. We illustrate our results with simulations and an application on fetopathologic data.