Nonparametric estimation of a periodic function

July, 1999
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Peter Hall, James Reimann, and John Rice
Annals of Probability vol. 29, pages 362-384 (2001)

Motivated by applications to light curves of periodic variable stars, we study nonparametric methods for estimating both the period and the amplitude function from noisy observations of a periodic function made at irregularly spaced times. It is shown that nonparametric estimators of period converge at parametric rates and attain a semiparametric lower bound which is the same if the shape of the periodic function is unknown as if it were known. Also, first-order properties of nonparametric estimators of the amplitude function are identical to those that would obtain if the period were known. Numerical simulations and applications to real data show the method to work well in practice.

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