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On the stability of maximum‐likelihood estimators of orthogonal parameters
Author(s) -
Cox D. R.,
Reid N.
Publication year - 1989
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 - 10.2307/3314851
Subject(s) - maximum likelihood , mathematics , estimator , statistics , likelihood function , neighbourhood (mathematics) , stability (learning theory) , m estimator , restricted maximum likelihood , point (geometry) , mathematical analysis , computer science , geometry , machine learning
If two parameters ψ and λ, are orthogonal, λψ, the maximum‐likelihood estimate of λ for given ψ, varies only slowly with ψ in the neighbourhood of the overall maximum‐likelihood point. The same is true if ψλ is replaced by a nonlinear function h (ψλ). The detailed form of the variation of ψλ with ψ is studied, and a basis suggested for choosing a particular function h (ψλ) that shows the dependence in the least informative fashion.