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On estimating the change point in generalized linear models

Kung-Yee Liang and Hongling Zhou

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Abstract

Statistical models incorporating change points are common in practice, especially in the area of biomedicine. This approach is appealing in that a specific parameter is introduced to account for the abrupt change in the response variable relating to a particular independent variable of interest. The statistical challenge one encounters is that the likelihood function is not differentiable with respect to this change point parameter. Consequently, the conventional asymptotic properties for the maximum likelihood estimators fail to hold in this situation. In this paper, we propose an estimating procedure for estimating the change point along with other regression coefficients under the generalized linear model framework. We show that the proposed estimators enjoy the conventional asymptotic properties including consistency and normality. Simulation work we conducted suggests that it performs well for the situations considered. We applied the proposed method to a case-control study aimed to examine the relationship between the risk of myocardial infarction and alcohol intake.

Chapter information

Source
N. Balakrishnan, Edsel A. Peña and Mervyn J. Silvapulle, eds., Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 305-320

Dates
First available in Project Euclid: 1 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1207058282

Digital Object Identifier
doi:10.1214/193940307000000239

Mathematical Reviews number (MathSciNet)
MR2462215

Subjects
Primary: 62F10: Point estimation 62F12: Asymptotic properties of estimators
Secondary: 62E20: Asymptotic distribution theory

Keywords
asymptotic normality change point consistency generalized linear model smoothing function

Rights
Copyright © 2008, Institute of Mathematical Statistics

Citation

Zhou, Hongling; Liang, Kung-Yee. On estimating the change point in generalized linear models. Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, 305--320, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/193940307000000239. https://projecteuclid.org/euclid.imsc/1207058282


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