ISSN:
1572-9052
Keywords:
Asymptotic expansions
;
index notation
;
invariant Taylor series expansions
;
likelihood
;
tensors
;
yokes
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Stochastic expansions of likelihood quantities are a basic tool for asymptotic inference. The traditional derivation is through ordinary Taylor expansions, rearranging terms according to their asymptotic order. The resulting expansions are called hereexpected/observed, being expressed in terms of the score vector, the expected information matrix, log likelihood derivatives and their joint moments. Though very convenient for many statistical purposes, expected/observed expansions are not usually written in tensorial form. Recently, within a differential geometric approach to asymptotic statistical calculations, invariant Taylor expansions based on likelihood yokes have been introduced. The resulting formulae are invariant, but the quantities involved are in some respects less convenient for statistical purposes. The aim of this paper is to show that, through an invariant Taylor expansion of the coordinates related to the expected likelihood yoke, expected/observed expansions up to the fourth asymptotic order may be re-obtained from invariant Taylor expansions. This derivation producesinvariant expected/observed expansions.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00773474
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