A NOTE ON THE ALMOST SURE CONVERGENCE OF CENTRAL ORDER
STATISTICS
Abstract: We prove almost sure versions of distributional limit theorems for central order
statistics. We develop a new method which not only gives a simplified proof of existing
results in the literature, but also extends them for general summation methods, leading to
considerably sharper results.
2000 AMS Mathematics Subject Classification: 60F05, 60F15, 40G99.
Key words and phrases: Central order statistics, almost sure limit theorem, summation
methods.