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arXiv · 1601.01434

On differentiability of implicitly defined function in semi-parametric profile likelihood estimation

Yuichi Hirose
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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. 2016-01-07. On differentiability of implicitly defined function in semi-parametric profile likelihood estimation. https://doi.org/10.3150/14-bej669

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