On differentiability of implicitly defined function in semi-parametric profile likelihood estimation
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.
Keywords
Cite
@article{arxiv.1601.01434,
title = {On differentiability of implicitly defined function in semi-parametric profile likelihood estimation},
author = {Yuichi Hirose},
journal= {arXiv preprint arXiv:1601.01434},
year = {2016}
}
Comments
Published at http://dx.doi.org/10.3150/14-BEJ669 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)