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Nonparametric maximum likelihood estimation of the structural mean of a sample of curves


Gervini, D; Gasser, T (2005). Nonparametric maximum likelihood estimation of the structural mean of a sample of curves. Biometrika, 92(4):801-820.

Abstract

A random sample of curves can be usually thought of as noisy realisations of a compound stochastic process X(t) = Z{W(t)}, where Z(t) produces random amplitude variation and W(t) produces random dynamic or phase variation. In most applications it is more important to estimate the so-called structural mean µ(t) = E{Z(t)} than the crosssectional mean E{X(t)}, but this estimation problem is difficult because the process Z(t) is not directly observable. In this paper we propose a nonparametric maximum likelihood estimator of µ(t). This estimator is shown to be {surd}n-consistent and asymptotically normal under the assumed model and robust to model misspecification. Simulations and a realdata example show that the proposed estimator is competitive with landmark registration, often considered the benchmark, and has the advantage of avoiding time-consuming and often infeasible individual landmark identification.

Abstract

A random sample of curves can be usually thought of as noisy realisations of a compound stochastic process X(t) = Z{W(t)}, where Z(t) produces random amplitude variation and W(t) produces random dynamic or phase variation. In most applications it is more important to estimate the so-called structural mean µ(t) = E{Z(t)} than the crosssectional mean E{X(t)}, but this estimation problem is difficult because the process Z(t) is not directly observable. In this paper we propose a nonparametric maximum likelihood estimator of µ(t). This estimator is shown to be {surd}n-consistent and asymptotically normal under the assumed model and robust to model misspecification. Simulations and a realdata example show that the proposed estimator is competitive with landmark registration, often considered the benchmark, and has the advantage of avoiding time-consuming and often infeasible individual landmark identification.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:04 Faculty of Medicine > Epidemiology, Biostatistics and Prevention Institute (EBPI)
Dewey Decimal Classification:610 Medicine & health
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Physical Sciences > General Mathematics
Life Sciences > Agricultural and Biological Sciences (miscellaneous)
Life Sciences > General Agricultural and Biological Sciences
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Physical Sciences > Applied Mathematics
Language:English
Date:December 2005
Deposited On:05 Jun 2009 15:49
Last Modified:29 Jul 2020 19:02
Publisher:Oxford University Press
ISSN:0006-3444
OA Status:Green
Publisher DOI:https://doi.org/10.1093/biomet/92.4.801
Official URL:http://biomet.oxfordjournals.org/cgi/reprint/92/4/801

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