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Changing Parameters by Partial Mappings

M. Wiedenbeck ; Nanny Wermuth (Institutionen för matematiska vetenskaper, matematisk statistik)
Statistica Sinica (1017-0405). Vol. 20 (2010), 2, p. 823-836.
[Artikel, refereegranskad vetenskaplig]

Changes between different sets of parameters are often needed in multivariate statistical modeling, such as transformations within linear regression or in exponential models. There may, for instance, be specific inference questions based on subject matter interpretations, alternative well-fitting constrained models, compatibility judgements of seemingly distinct constrained models, or different reference priors under alternative parameterizations. We introduce and discuss a partial mapping, called partial replication, and relate it to a more complex mapping, called partial inversion. Both operations are used to decompose matrix operations, to explain recursion relations among sets of linear parameters, to change between different types of linear models, to approximate maximum-likelihood estimates in exponential family models under independence constraints, and to switch partially between sets of canonical and moment parameters in exponential family distributions or between sets of corresponding maximum-likelihood estimates.

Nyckelord: Exponential family, independence constraints, matrix operators, partial, inversion, partial replication, reduced model estimates, REML-estimates, sandwich estimates, SEEMINGLY UNRELATED REGRESSIONS, LIKELIHOOD, MODELS, GRAPHS, INDEPENDENCE, VARIABLES, DISCRETE, SYSTEMS, TESTS



Denna post skapades 2010-05-27. Senast ändrad 2012-03-19.
CPL Pubid: 121980

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)

Ämnesområden

Matematisk statistik

Chalmers infrastruktur