The law of the large numbers for U-statistics for 2m-wise independent random variables

✍ Scribed by Miguel A. Arcones

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 240 KB
• Volume: 40
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(98)00108-4

✦ Synopsis

The strong law of the large numbers for U-statistics has been proved for a sequence of independent random variables using martingale techniques. We see that the condition of independence can be relaxed to 2m-wise independence. In this case martingale techniques cannot be applied. We also consider Marcinkiewicz laws of large numbers for U-statistics for a special case. (~) 1998 Elsevier Science B.V. All rights reserved