Nonparametric maximum likelihood estimation of the structural mean of a sample of curves
成果类型：
Article
署名作者：
Gervini, D; Gasser, T
署名单位：
University of Wisconsin System; University of Wisconsin Milwaukee; University of Zurich
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/92.4.801
发表日期：
2005
页码：
801820
关键词：
摘要：
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 mu(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 mu(t). This estimator is shown to be root 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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