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The linear model with variance-covariance components and jackknife estimation

Jaromír Kudeláš — 1994

Applications of Mathematics

Let $θ^{*}$ be a biased estimate of the parameter $ϑ$ based on all observations $x_{1}$ , $\dots$ , $x_{n}$ and let $θ_{- i}^{*}$ ( $i = 1, 2, \dots, n$ ) be the same estimate of the parameter $ϑ$ obtained after deletion of the $i$ -th observation. If the expectation of the estimators $θ^{*}$ and $θ_{- i}^{*}$ are expressed as $\begin{matrix} E (θ^{*}) & = ϑ + a (n) b (ϑ) \\ E (θ_{- i}^{*}) & = ϑ + a (n - 1) b (ϑ) i = 1, 2, \dots, n, \end{matrix}$ where $a (n)$ is a known sequence of real numbers and $b (ϑ)$ is a function of $ϑ$ , then this system of equations can be regarded as a linear model. The least squares method gives the generalized jackknife estimator. Using this method, it is possible to obtain the unbiased...

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