Nonparametric maximum likelihood estimation of the structural mean of a sample of curves
Gervini, D.
In: Biometrika, 2005, vol. 92, no. 4, p. 801-820
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- 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