Consider a triangular array of mean zero Gaussian random variables. Under some weak conditions this paper proves that the partial sums and the point processes of exceedances formed by the array are asymptotically independent. For a standardized stationary Gaussian sequence, it is shown under some mild conditions that the point process of exceedances formed by the sequence (after centered at the sample mean) converges in distribution to a Poisson process and it is asymptotically independent of the partial sums. Finally, the joint limiting distributions of the extreme order statistics and the partial sums are obtained.
Bibliographical noteFunding Information:
Yongcheng Qi’s research was supported by NSF grant DMS 0604176.
- Extreme order statistics
- Joint distribution
- Partial sum
- Point process of exceedances
- Stationary Gaussian sequence