Title: A note on the completeness of the normal family with constant coefficient of variation
Abstract: Suppose that Z1 …Zn are independent and normally distributed with common mean u and variance σ2.When σ2 = λμ2with given λ> 0, it is well known that the minimal sufficient statistic is not complete for μ if n ≥ 2. The question of completeness seems to be unresolved when n = 1. In this note, we consider this case and, by using the heat equation, establish the second moment completeness of the minimal sufficient statistic, a property which is weaker than completeness but stronger than bounded completeness. Finally, we apply this result to a linear calibration problem.
Publication Year: 1988
Publication Date: 1988-01-01
Language: en
Type: article
Indexed In: ['crossref']
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