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The role of reversals in order‐restricted inference
Author(s) -
Perlman Michael D.,
Chaudhuri Sanjay
Publication year - 2004
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 - 10.2307/3315942
Subject(s) - monotonic function , cone (formal languages) , inference , estimator , statistical inference , mathematics , order (exchange) , regular polygon , property (philosophy) , maximum likelihood , convex cone , euclidean space , space (punctuation) , stochastic ordering , mathematical economics , econometrics , statistics , combinatorics , computer science , convex optimization , mathematical analysis , algorithm , geometry , economics , convex combination , artificial intelligence , philosophy , finance , epistemology , operating system
A statistical model is said to be an order‐restricted statistical model when its parameter takes its values in a closed convex cone C of the Euclidean space. In recent years, order‐restricted likelihood ratio tests and maximum likelihood estimators have been criticized on the grounds that they may violate a cone order monotonicity (COM) property, and hence reverse the cone order induced by C. The authors argue here that these reversals occur only in the case that C is an obtuse cone, and that in this case COM is an inappropriate requirement for likelihood‐based estimates and tests. They conclude that these procedures thus remain perfectly reasonable procedures for order‐restricted inference.