Nonparametric maximum likelihood estimation for shifted curves
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2001 · Volume 63 · Issue 2
Abstract
The analysis of a sample of curves can be done by self-modelling regression methods. Within this framework we follow the ideas of nonparametric maximum likelihood estimation known from event history analysis and the counting process set-up. We derive an infinite dimensional score equation and from there we suggest an algorithm to estimate the shape function for a simple shape invariant model. The nonparametric maximum likelihood estimator that we find turns out to be a Nadaraya–Watson-like estimator, but unlike in the usual kernel smoothing situation we do not need to select a bandwidth or even a kernel function, since the score equation automatically selects the shape and the smoothing parameter for the estimation. We apply the method to a sample of electrophoretic spectra to illustrate how it works.
Keywords
Curve alignment, Fréchet differentiation, Nonparametric maximum likelihood estimation, Sample of curves, Semiparametric models
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