Efficient Semiparametric Estimation of the Periods in a Superposition of Periodic Functions with Unknown Shape
Élisabeth Gassiat, Céline Lévy‐Leduc · Journal of Time Series Analysis · 2006
Abstract. We consider the estimation of the periods of periodic functions when their shape is unknown and they are corrupted by Gaussian white noise. In the case of a single periodic function, we propose a consistent and asymptotically efficient semiparametric estimator of the period. We then study the case of a sum of two periodic functions of unknown shape with different periods and propose semiparametric estimators of their periods that are consistent and asymptotically Gaussian.