Let ${\theta }^{*}$ be a biased estimate of the parameter $\vartheta$ based on all observations $x_1$, $\cdots$, $x_n$ and let ${\theta }_{-i}^{*}$ ($i=1,2,\cdots ,n$) be the same estimate of the parameter $\vartheta$ obtained after deletion of the $i$-th observation. If the expectation of the estimators ${\theta }^{*}$ and ${\theta }_{-i}^{*}$ are expressed as $$\begin{array}{cc}\hfill \mathrm{E}\left({\theta }^{*}\right)& =\vartheta +a\left(n\right)b\left(\vartheta \right)\hfill \\ \hfill \mathrm{E}\left({\theta }_{-i}^{*}\right)& =\vartheta +a(n-1)b\left(\vartheta \right)i=1,2,\cdots ,n,\hfill \end{array}$$ where $a\left(n\right)$ is a known sequence of real numbers and $b\left(\vartheta \right)$ is a function of $\vartheta$, 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 aim of this paper is to characterize the Multivariate Gauss-Markoff model $\left(MGM\right)$ as in () with singular covariance matrix and missing values. $MGMDP2$ model and completed $MGMDP2Q$ model are obtained by three transformations $D$, $P$ and $Q$ (cf. ()) of $MGM$. The unified theory of estimation (Rao, 1973) which is of interest with respect to $MGM$ has been used. The characterization is reached by estimation of parameters: scalar ${\sigma }^2$ and linear combination ${\lambda }^{\text{'}}\overline{B}$ ( $\overline{B}=vecB)$ as in (), (), () as well as by the model of the form ()...