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August 2003 Large sample theory for semiparametric regression models with two-phase, outcome dependent sampling
Norman Breslow, Brad McNeney, Jon A. Wellner
Ann. Statist. 31(4): 1110-1139 (August 2003). DOI: 10.1214/aos/1059655907

Abstract

Outcome-dependent, two-phase sampling designs can dramatically reduce the costs of observational studies by judicious selection of the most informative subjects for purposes of detailed covariate measurement. Here we derive asymptotic information bounds and the form of the efficient score and influence functions for the semiparametric regression models studied by Lawless, Kalbfleisch and Wild (1999) under two-phase sampling designs. We show that the maximum likelihood estimators for both the parametric and nonparametric parts of the model are asymptotically normal and efficient. The efficient influence function for the parametric part agrees with the more general information bound calculations of Robins, Hsieh and Newey (1995). By verifying the conditions of Murphy and van der Vaart (2000) for a least favorable parametric submodel, we provide asymptotic justification for statistical inference based on profile likelihood.

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Norman Breslow. Brad McNeney. Jon A. Wellner. "Large sample theory for semiparametric regression models with two-phase, outcome dependent sampling." Ann. Statist. 31 (4) 1110 - 1139, August 2003. https://doi.org/10.1214/aos/1059655907

Information

Published: August 2003
First available in Project Euclid: 31 July 2003

zbMATH: 1105.62335
MathSciNet: MR2001644
Digital Object Identifier: 10.1214/aos/1059655907

Subjects:
Primary: 60F05, 60F17
Secondary: 60J65, 60J70

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 4 • August 2003
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