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I recently ran into a kind of integral that I've never encountered before.

How should the following integral be expressed as a "normal" double integral?

$\iint \mathrm d f(u,v)$ where $f:\mathbb{R}^2\rightarrow \mathbb{R}$

The only thing I can think of that might be correct is $\iint \frac{\partial f}{\partial u} \frac{\partial f}{\partial v} \mathrm du \ \mathrm dv$ but I cannot motivate this and I've had no luck with my reference books nor with Google.

[Edit]

The following comes from http://dx.doi.org/10.1006/jmva.1994.1031

$\hat V(t) = n(1-\hat F_n(t))^2 \int_0^t\int_0^t \frac{d\hat H_n(u,v)}{Y_n(u) Y_n(v)}$

where $\hat F_n(t) \in \mathbb{R}$ is a distribution function, $Y_n(t) \in \mathbb{N}$ is a count and $\hat H_n$ is defined as $\hat H_n(s,t) = \frac{1}{n}\sum_{i=1}^m\sum_{j=1}^{K_i}\sum_{l=1}^{K_i} \left\{ I_{(Z_{ij}\le s,\Delta_{ij}=1)} - \int_0^s I_{(Z_{ij}\ge u)} d\hat\Lambda_n(u) \right\} $ $ \times \left\{ I_{(Z_{il}\le t,\Delta_{il}=1)} - \int_0^t I_{(Z_{il}\ge u)} d\hat\Lambda_n(u) \right\}$

where $I\in \{0,1\}$ is the indicator function and $\hat\Lambda_n \in \mathbb{R}$ is the so-called Nelson estimator. $Z_{ij} \in \mathbb{R}$ is a time and $\Delta_{ij} \in \{0,1\}$ is a censoring indicator.

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    Thanks for posting the details, but I'm still at a loss. Sorry!2011-10-19

0 Answers 0