### 10.7.2 Heuristic Justification for the Jackknife and the Bootstrap

Let us first justify the validity of the bootstrap estimate. In the arguments given here we denote n−1/2Δn = FnF by Dn and ${F}_{n}^{*}-{F}_{n}$ by ${D}_{n}^{*}$. We can simplify notations by writing $\int {T}^{\prime }\left(x;F\right)d{D}_{n}\left(x\right)$ by ${L}_{F}\left({D}_{n}\right)$ and $\int {T}^{\prime \prime }\left({x}_{1},{x}_{2};F\right)d{D}_{n}\left({x}_{1}\right)d{D}_{n}\left({x}_{2}\right)$ by ${Q}_{F}\left({D}_{n}\right)$. If we expand $T\left({F}_{n}^{*}\right)$ about Fn, then we have

$\begin{array}{l}\hfill T\left({F}_{n}^{*}\right)\end{array}$

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