A New Class of Asymptotically Distribution-Free Smooth Tests

TL;DR

This paper introduces a new family of smooth goodness-of-fit tests that are asymptotically distribution-free, robust to parameter estimation and model selection, and computationally efficient compared to bootstrap methods.

Contribution

The authors develop a novel class of smooth tests leveraging empirical process theory that maintain distribution-free properties under practical conditions.

Findings

Tests are asymptotically distribution-free even with parameter estimation.

The proposed methods are effective with moderately large sample sizes.

A computationally efficient alternative to bootstrap is presented.

Abstract

This article demonstrates how recent developments in the theory of empirical processes allow us to construct a new family of asymptotically distribution-free smooth tests. Their distribution-free property is preserved even when the parameters are estimated, model selection is performed, and the sample size is only moderately large. A computationally efficient alternative to the classical parametric bootstrap is also discussed.