Jump detection in generalized error-in-variables regression with an application to Australian health tax policies

TL;DR

This paper introduces a new nonparametric method for detecting jump points in regression models with measurement errors, applicable to real-world policy analysis such as Australian health taxes.

Contribution

It proposes a novel error-in-variables jump estimator that does not require parametric assumptions on measurement errors, with demonstrated theoretical and numerical validation.

Findings

Effective jump detection in error-prone predictors

Theoretical guarantees of the estimator's performance

Application to Australian health policy data

Abstract

Without measurement errors in predictors, discontinuity of a nonparametric regression function at unknown locations could be estimated using a number of existing approaches. However, it becomes a challenging problem when the predictors contain measurement errors. In this paper, an error-in-variables jump point estimator is suggested for a nonparametric generalized error-in-variables regression model. A major feature of our method is that it does not impose any parametric distribution on the measurement error. Its performance is evaluated by both numerical studies and theoretical justifications. The method is applied to studying the impact of Medicare Levy Surcharge on the private health insurance take-up rate in Australia.