Can the finiteness of a mean be tested?

✍ Scribed by D.L. Hawkins

• Book ID: 104302466
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 234 KB
• Volume: 32
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(96)00084-3

✦ Synopsis

Let ff,,(o~) denote the set of absolutely continuous distributions on [0, o~) with finite (infinite) mean. We show the non-existence of a test of H0: F C fin versus Hi: F E dgm in the class of sequential tests based on independent identically distributed observations X1,X2 .... distributed as F, and which make the right decision with arbitrarily high probability and have finite stopping times almost surely. This result is obtained using the distinguishability theory of Hoeffding and Wolfowitz (1958).