  Let $\mathbf{X}=\{X_{n}\}_{n\geq 1}$ be a sequence of stationary Gaussian
variables and suppose that only some of the random variables from $\mathbf{X}$
can be observed. In this paper, by studying the limiting properties of
multidimensional exceedance point processes for $\mathbf{X}$, we derived the
joint limit distribution of extreme order statistics for the Gaussian sequence
$\mathbf{X}$ and its observed ones. The joint limit distribution of the
locations and heights of the maxima for the Gaussian sequence $\mathbf{X}$ and
its observed ones are also obtained.
