In this chapter, we build on the presentation of the functional delta method given in Section 2.2.4. Recall the concept of Hadamard differentiability introduced in this section and also defined more precisely in Section 6.3. The key result of Section 2.2.4 is that the delta method and its bootstrap counterpart work provided the map φ is Hadamard differentiable tangentially to a suitable set D0. We first present in Section 12.1 clarifications and proofs of the two main theorems given in Section 2.2.4, the functional delta method for Hadamard differentiable maps (Theorem 2.8 on Page 22) and the conditional analog for the bootstrap (Theorem 2.9 on Page 23). We then give in Section 12.2 several important examples of Hadamard differentiable maps of use in statistics, along with specific illustrations of how those maps are utilized.


Volterra Integral Equation Delta Method Independent Increment Censor Survival Data Conditional Analog 
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© Springer Science+Business Media, LLC 2008

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