半参数轮廓似然估计中隐定义函数的可微性
On differentiability of implicitly defined function in semi-parametric profile likelihood estimation
摘要：
本文研究了半参数模型参数的轮廓似然估计中所遇到的隐定义函数的可微性。Scott和Wild（Biometrika 84（1997）57-71; J. Statist.计划Inference 96（2001）3-27）以及Murphy和van der Vaart（J. Amer. Statistist. Assoc.95（2000）449-485）开发了可以通过参数化轮廓似然中的参数并在半参数模型中使用近似的最不利子模型来避免处理这种隐式定义的函数的方法。我们的结果表明，Hirose（Ann. Inst. Statistist. 63（2011）1247-1275），其使用简档似然的直接扩展。
英文摘要：
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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