Fisher information, sufficiency, and ancillarity: some clarifications

Nitis Mukhopadhyay () and Swarnali Banerjee ()

METRON, 2013, vol. 71, issue 1, 33-38

Abstract: Misconceptions are many when it comes to Fisher information, sufficiency, and ancillarity, especially among beginners. Many believe that $$\mathcal I _{T_{1}}(\theta )+\mathcal I _{T_{2}}(\theta )$$ should equal $$\mathcal I _{T_{1}+T_{2}}(\theta )$$ for all $$\theta $$ . We exhibit precise scenarios where $$\mathcal I _{T_{1}+T_{2}}(\theta )$$ is $$>, =,$$ or $$>\mathcal I _{T_{1}}(\theta )+\mathcal I _{T_{2}}(\theta )$$ for all $$\theta $$ . Then, we clarify the process of verifying ancillarity of a statistic with concrete examples. Copyright Sapienza Università di Roma 2013

Keywords: Ancillarity; Dependent observations; Independent observations; Information; Sufficiency; 62B05; 62B10; 62-01 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s40300-013-0005-0

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