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Nonparametric Maximum Likelihood Estimation of the Structural Mean of a Sample of Curves

Daniel Gervini and Theo Gasser
Biometrika
Vol. 92, No. 4 (Dec., 2005), pp. 801-820
Published by: Oxford University Press on behalf of Biometrika Trust
Stable URL: http://www.jstor.org/stable/20441237
Page Count: 20
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Nonparametric Maximum Likelihood Estimation of the Structural Mean of a Sample of Curves
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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 cross-sectional 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 √n-consistent and asymptotically normal under the assumed model and robust to model misspecification. Simulations and a real-data 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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