Bootstrap-Based Goodness-of-Fit Test for Parametric Families of Conditional Distributions

TL;DR

This paper introduces a bootstrap-based goodness-of-fit test for distributional regression that compares nonparametric and semi-parametric estimates of the marginal distribution, demonstrating superior power in certain scenarios without hyperparameters.

Contribution

It presents a new, hyperparameter-free goodness-of-fit test for parametric families of conditional distributions using bootstrap methods, improving detection of deviations.

Findings

Test outperforms existing methods in power

No hyperparameters required for implementation

Easily applicable using R package gofreg

Abstract

A consistent goodness-of-fit test for distributional regression is introduced. The test statistic is based on a process that traces the difference between a nonparametric and a semi-parametric estimate of the marginal distribution function of Y. As its asymptotic null distribution is not distribution-free, a parametric bootstrap method is used to determine critical values. Empirical results suggest that, in certain scenarios, the test outperforms existing specification tests by achieving a higher power and thereby offering greater sensitivity to deviations from the assumed parametric distribution family. Notably, the proposed test does not involve any hyperparameters and can easily be applied to individual datasets using the gofreg-package in R.