Journal article
On the convergence of Newton's method when estimating higher dimensional parameters
Journal of Multivariate Analysis, Vol.98(5), pp.916-931
2007
Abstract
In this paper, we consider the estimation of a parameter of interest where the estimator is one of the possibly several solutions of a set of nonlinear empirical equations. Since Newton's method is often used in such a setting to obtain a solution, it is important to know whether the so obtained iteration converges to the locally unique consistent root to the aforementioned parameter of interest. Under some conditions, we show that this is eventually the case when starting the iteration from within a ball about the true parameter whose size does not depend on n. Any preliminary almost surely consistent estimate will eventually lie in such a ball and therefore provides a suitable starting point for large enough n. As examples, we will apply our results in the context of M-estimates, kernel density estimates, as well as minimum distance estimates.
Details
- Title
- On the convergence of Newton's method when estimating higher dimensional parameters
- Authors/Creators
- B.R. Clarke (Author/Creator)A. Futschik (Author/Creator)
- Publication Details
- Journal of Multivariate Analysis, Vol.98(5), pp.916-931
- Publisher
- Academic Press
- Identifiers
- 991005545154607891
- Copyright
- © 2007 Elsevier Inc.
- Murdoch Affiliation
- School of Chemical and Mathematical Science
- Language
- English
- Resource Type
- Journal article
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- Collaboration types
- Domestic collaboration
- International collaboration
- Citation topics
- 9 Mathematics
- 9.92 Statistical Methods
- 9.92.220 Robust Estimation
- Web Of Science research areas
- Statistics & Probability
- ESI research areas
- Mathematics