Efficient semi-parametric estimation of the periods in a superposition of
periodic functions with unknown shape
Elisabeth Gassiat and Celine Levy-Leduc
Journal of Time Series Analysis
We consider the estimation of the periods from a
sum of periodic functions of unknown shape
corrupted by Gaussian white noise. In the case of a single periodic signal,
we propose a consistent and asymptotically efficient
semiparametric estimator of the period. We then study the case of a
sum of two periodic signals of unknown shape with different periods.
For a large class of signals, we propose
semiparametric estimators of the two periods
that are consistent and asymptotically Gaussian.