Equivalence of the Higher-order Asymptotic Efficiency of k-step and Extremum Statistics

Donald Andrews ()

No 1269, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: It is well known that a one-step scoring estimator that starts from any N^{1/2}-consistent estimator has the same first-order asymptotic efficiency as the maximum likelihood estimator. This paper extends this result to k-step estimators and test statistics for k >= 1, higher-order asymptotic efficiency, and general extremum estimators and test statistics. The paper shows that a k-step estimator has the same higher-order asymptotic efficiency, to any given order, as the extremum estimator towards which it is stepping, provided (i) k is sufficiently large, (ii) some smoothness and moment conditions hold, and (iii) a condition on the initial estimator holds. For example, for the Newton-Raphson k-step estimator, we obtain asymptotic equivalence to integer order s provided 2^{k} >= s + 1. Thus, for k = 1, 2, and 3, one obtains asymptotic equivalence to first, third, and seventh orders respectively. This means that the maximum differences between the probabilities that the (N^{1/2}-normalized) k-step and extremum estimators lie in any convex set are o(1), o(N^{-3/2}), and o(N^{-3}) respectively.

Keywords: Asymptotics; Edgeworth expansion; extremum estimator; Gauss-Newton; higher-order efficiency; Newton-Raphson.; Inventory theory; optimal ordering policies; (S; s) policies; K-concavity (search for similar items in EconPapers)
JEL-codes: C12 C13 (search for similar items in EconPapers)
Pages: 42 pages
Date: 2000-07
Note: CFP 1044.
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Published in Econometric Theory (2002), 18: 1040-1085

Downloads: (external link)
https://cowles.yale.edu/sites/default/files/files/pub/d12/d1269.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found

Related works:
Journal Article: EQUIVALENCE OF THE HIGHER ORDER ASYMPTOTIC EFFICIENCY OF k-STEP AND EXTREMUM STATISTICS (2002)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cwl:cwldpp:1269

Ordering information: This working paper can be ordered from
Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
The price is None.

Access Statistics for this paper

More papers in Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University Yale University, Box 208281, New Haven, CT 06520-8281 USA. Contact information at EDIRC.
Bibliographic data for series maintained by Brittany Ladd ().