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February 2016 On differentiability of implicitly defined function in semi-parametric profile likelihood estimation
Yuichi Hirose
Bernoulli 22(1): 589-614 (February 2016). DOI: 10.3150/14-BEJ669

Abstract

In this paper, we study the differentiability of implicitly defined functions which we encounter in the profile likelihood estimation of parameters in semi-parametric models. Scott and Wild (Biometrika 84 (1997) 57–71; J. Statist. Plann. Inference 96 (2001) 3–27) and Murphy and van der Vaart (J. Amer. Statist. Assoc. 95 (2000) 449–485) developed methodologies that can avoid dealing with such implicitly defined functions by parametrizing parameters in the profile likelihood and using an approximate least favorable submodel in semi-parametric models. Our result shows applicability of an alternative approach presented in Hirose (Ann. Inst. Statist. Math. 63 (2011) 1247–1275) which uses the direct expansion of the profile likelihood.

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Yuichi Hirose. "On differentiability of implicitly defined function in semi-parametric profile likelihood estimation." Bernoulli 22 (1) 589 - 614, February 2016. https://doi.org/10.3150/14-BEJ669

Information

Received: 1 August 2013; Revised: 1 April 2014; Published: February 2016
First available in Project Euclid: 30 September 2015

zbMATH: 06543281
MathSciNet: MR3449794
Digital Object Identifier: 10.3150/14-BEJ669

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

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Vol.22 • No. 1 • February 2016
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