The joint limit properties of point process of exceedances and partial sums of Gaussian sequences subject to missing observations

In this paper, we first prove that the point processes of exceedances formed by a Gaussian triangular array subject to missing observations and the partial sums are asymptotically independent under some mild conditions. Applying the obtained results, we derive the joint limit properties of the point process of exceedances formed by stationary Gaussian sequences subject to missing observations and centered at the sample mean and the partial sums. As a by-product, the asymptotic joint limit distributions of order statistics from Gaussian sequences subject to missing observations and the partial sums are obtained.