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Can the finiteness of a mean be tested?

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  • Hawkins, D. L.

Abstract

Let denote the set of absolutely continuous distributions on [0, [infinity]) with finite (infinite) mean. We show the non-existence of a test of H0: versus 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).

Suggested Citation

  • Hawkins, D. L., 1997. "Can the finiteness of a mean be tested?," Statistics & Probability Letters, Elsevier, vol. 32(3), pages 273-277, March.
    • Handle: RePEc:eee:stapro:v:32:y:1997:i:3:p:273-277
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    References listed on IDEAS

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    1. Milbrodt H. & Strasser H., 1984. "Distinguishability And Invariance," Statistics & Risk Modeling, De Gruyter, vol. 2(1-2), pages 93-110, February.
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