MLE, Information, Ancillary Complement, and Conditional Inference with Illustrations

Nitis Mukhopadhyay () and Yan Zhuang ()
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Nitis Mukhopadhyay: University of Connecticut
Yan Zhuang: University of Connecticut

Methodology and Computing in Applied Probability, 2017, vol. 19, issue 2, 615-629

Abstract: Abstract Fisher’s (Proceedings of Royal Society Series A 144, 285–307 1934, 1956) example remains a classic where the maximum likelihood estimator (T) was non-sufficient, had less than full information, but an ancillarity complement (S) helped in recovering the full information I ( T , S ) ( 𝜃 ) $\mathcal {I}_{(T,S)}(\theta )$ . In the absence of other readily accessible easy-to-grasp examples of similar nature, we begin with general calculations for useful information entities, both unconditional ( I T ( 𝜃 ) $\mathcal {I}_{T}(\theta )$ ) and conditional ( I T ∣ S ( 𝜃 ) $\mathcal {I}_{T\mid S}(\theta )$ ). These have led us to propose a number of new illustrations in the spirit of the original example. Then, we introduce a multivariate data extension of the original example with an illustration. We wrap up this investigation with an example of a non-sufficient MLE T that has (i) the full Fisher information, and (ii) has an ancillary complement S.

Keywords: Ancillary complement; Conditional inference; Full information; Information; Maximum likelihood estimator; Multivariate extension; Non-sufficiency; Sufficiency; 62B05; 62B10; 62B86 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s11009-016-9529-0

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