The Annals of Applied Statistics

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

Yicheng Kang, Xiaodong Gong, Jiti Gao, and Peihua Qiu

Full-text: Open access

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.

Article information

Source
Ann. Appl. Stat., Volume 9, Number 2 (2015), 883-900.

Dates
Received: October 2014
Revised: February 2015
First available in Project Euclid: 20 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1437397116

Digital Object Identifier
doi:10.1214/15-AOAS814

Mathematical Reviews number (MathSciNet)
MR3371340

Zentralblatt MATH identifier
06499935

Keywords
Bandwidth selection demand for private health insurance exponential family generalized regression kernel smoothing measurement errors

Citation

Kang, Yicheng; Gong, Xiaodong; Gao, Jiti; Qiu, Peihua. Jump detection in generalized error-in-variables regression with an application to Australian health tax policies. Ann. Appl. Stat. 9 (2015), no. 2, 883--900. doi:10.1214/15-AOAS814. https://projecteuclid.org/euclid.aoas/1437397116


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Supplemental materials

  • Supplement to “Jump detection in generalized error-in-variables regression with an application to Australian health tax policies”. This supplemental file mainly gives the proof of Theorem 1.