A note on the empirical distribution of dependent random variables

✍ Scribed by D.L. Hanson; Gang Li

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 131 KB
• Volume: 34
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(96)00198-8

✦ Synopsis

approximation and various other sequential procedures, the question of whether suplD~(t) I ---, 0 a.s.

(1) t arises. For each t, D,(t) converges to 0 a.s., and by the Glivenko-Cantelli theorem (1) holds if {Y,} is i.i.d. We give an example showing that without the assumption of independence (1) might fail to hold.