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- Title
MLE, Information, Ancillary Complement, and Conditional Inference with Illustrations.
- Authors
Mukhopadhyay, Nitis; Zhuang, Yan
- 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 $\mathcal {I}_{(T,S)}(\theta )$ . 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 ( $\mathcal {I}_{T}(\theta )$ ) and conditional ( $\mathcal {I}_{T\mid S}(\theta )$ ). 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.
- Subjects
MEDIATED learning experience; MAXIMUM likelihood statistics; FISHER information; MULTIVARIATE analysis; FIELD extensions (Mathematics)
- Publication
Methodology & Computing in Applied Probability, 2017, Vol 19, Issue 2, p615
- ISSN
1387-5841
- Publication type
Article
- DOI
10.1007/s11009-016-9529-0