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Invariants and likelihood ratio statistics. (English) Zbl 0615.62041

Author’s summary: Because the likelihood ratio statistic is invariant under reparameterization, it is possible to make a large-sample expansion of the statistic itself and of its expectation in terms of invariants. In particular, the Bartlett adjustment factor can be expressed in terms of invariant combinations of cumulants of the first two log-likelihood derivatives. Such expansions are given, first for a scalar parameter and then for vector parameters. Geometrical interpretation is given where possible and some special cases are discussed.
Reviewer: A.Földes

MSC:

62F99 Parametric inference
62F12 Asymptotic properties of parametric estimators
62E20 Asymptotic distribution theory in statistics
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