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Update paper/paper.tex
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Co-authored-by: Nadia <[email protected]>
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ayushpatnaikgit and nadiaenh authored May 19, 2024
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Expand Up @@ -233,7 +233,7 @@ \subsection{Jackknife}

This object can be passed to estimators to obtain an estimate of variance alongside the point estimate.

$\hat{\theta}$ represents the estimator computed using the original weights, and $\hat{\theta_{(hj)}}$ represents the estimator computed from the replicate weights obtained when PSU $j$ from cluster $h$ is removed. The variance is given by:
$\hat{\theta}$ represents the estimator computed using the original weights, and $\hat{\theta_{(hj)}}$ represents the estimator computed from the replicate weights obtained when PSU $j$ from cluster $h$ is removed. The variance is estimated as:

\begin{equation}
\hat{V}_{\text{JK}}(\hat{\theta}) = \sum_{h = 1}^H \dfrac{n_h - 1}{n_h}\sum_{j = 1}^{n_h}(\hat{\theta}_{(hj)} - \hat{\theta})^2
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