Exercise1.1 Let Y1, ...,Yn be arandomsamplefromaPoissondistribution Pois(). InExample1.6, we foundthat T(Y) = ni =1Yi is asufficientstatisticfor
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Exercise1.1 Let Y1, ...,Yn be arandomsamplefromaPoissondistribution Pois(λ). InExample1.6, we foundthat T(Y) = Σni
=1Yi is asufficientstatisticfor λ using theFisher–Neymanfactorization theorem.
1. Obtain thisresultdirectlyusingthedefinitionofasufficientstatistic.Whatisthedistributionof T(Y)?
2. ∗Showthat T(Y) is aminimalsufficientstatisticfor λ.
3. ∗Showthat T(Y) is completeusing
(a) the definitionofacompletestatistic.
(b) the propertiesoftheexponentialfamilyofdistributions.
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Related Book For
Statistical Theory A Concise Introduction Texts In Statistical Science
ISBN: 9781032007458
2nd Edition
Authors: Felix Abramovich, Ya'acov Ritov
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