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The score function and a comparison of various adjustments of the profile likelihood
Author(s) -
Davison A. C.,
Stafford J. E.
Publication year - 1998
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315679
Subject(s) - score , statistics , mathematics , likelihood function , variance (accounting) , function (biology) , maximum likelihood , restricted maximum likelihood , score test , term (time) , econometrics , simple (philosophy) , physics , economics , biology , philosophy , accounting , epistemology , quantum mechanics , evolutionary biology
Several adjustments of the profile likelihood have the common effect of reducing the bias of the associated score function. Hence expansions for the adjusted score functions differ by a term, D ξ , that has small asymptotic order ( n −½ ). The effect of D ξ on other quantities of interest is studied. In particular, we find the bias and variance of the adjusted maximum‐likelihood estimate to be relatively unaffected, while differences in the Bartlett correction depend on D ξ in a simple way.