A Note on Properties of Iterative Procedures of Asymptotic Inference |
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Authors: | HCH Paardekooper HBA Steens G van der Hoek |
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Institution: | Operations Research Department, ABN, O.D. 60, P.O. Box 669, NL–1000 EG Amsterdam, The Netherlands;Financial Management Department, Moret Advies, Europalaan 450, NL–3526 KS Utrecht, The Netherlands;"De Driestar", P.O. Box 1093, NL–2800 BB Gouda, The Netherlands |
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Abstract: | This note deals with the article 'On iterative procedures of asymptotic inference' by K.O. DZHAPARIDZE (1983), in which an informal discussion is given on performing an unconstrained maximization or solving non–linear equations of statistics by iterative methods with the quadratic termination property. It discusses the theorem that if a maximized function, e.g. the likelihood function, is asymptotically quadratic, then for asymptotically efficient inference finitely many iterations are needed. It is argued here that the theory still applies if certain well specified inexact (hence computationally cheaper) line searches are used in the optimization. |
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Keywords: | Newton's method Quasi–Newton methods inexact line search maximum likelihood estimators Fisher's information matrix |
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