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Talk:Invariant estimator

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This is an old revision of this page, as edited by Melcombe (talk | contribs) at 09:41, 30 May 2008 (→non-Bayesian?). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.
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Equivariant?

Can someone say where the term "equivariant" has been used ... it is not in any of my dictionaries of maths or stats. Melcombe (talk) 09:32, 12 May 2008 (UTC)[reply]

It appears, for example, in Lehmann and Casella, Theory of Point Estimation. --Zvika (talk) 18:17, 12 May 2008 (UTC)[reply]

non-Bayesian?

Should such prominence be given to "non-Bayesian"? After all ideas of invariance can be applied to Bayesian estimation just as well. Consider for example HPD (highest posterior density) estimation (either point or interval estimates), which is not invariant to transformation of the parameters. Melcombe (talk) 09:14, 19 May 2008 (UTC)[reply]

Can you provide a source dealing with Bayesian equivariant estimators? I haven't encountered one. --Zvika (talk) 18:33, 19 May 2008 (UTC)[reply]
I am not sure that it is important to actually find examples of invariant Bayesian estimators, just that the idea of invariance can be applied to estimation in a Bayesian setting, where this would go beyond the impractical definition given in Bayesian estimation since contexts with prescribed loss functions are rare. Thus things like Maximum a posteriori need to be included as Bayesian estimates, and also the expectation of the posterior distribution, both in contexts of no-loss-function. Obviously HPD estimates are not invariant to transformations of the parameter space, and nor are expected values of the posterior, and it is important to be able to say this. Melcombe (talk) 09:41, 30 May 2008 (UTC)[reply]
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