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Efficient estimation for a subclass of shape invariant models. (English) Zbl 1189.62057
Summary: We observe a fixed number of unknown \(2\pi \)-periodic functions differing from each other by both phase and amplitude. This semiparametric model appears in the literature under the name “shape invariant model.” While the common shape is unknown, we introduce an asymptotically efficient estimator of the finite-dimensional parameters (phase and amplitude) using profile likelihood and Fourier basis. Moreover, this estimation method leads to a consistent and asymptotically linear estimator for the common shape.

62G05 Nonparametric estimation
62F12 Asymptotic properties of parametric estimators
62G20 Asymptotic properties of nonparametric inference
62J02 General nonlinear regression
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