Nonparametric estimation of a periodic sequence in the presence of a smooth trend. (English) Zbl 1285.62047

Vogt, Michael; Linton, Oliver

Biometrika 101, No. 1, 121-140 (2014).

Summary: We investigate a nonparametric regression model including a periodic component, a smooth trend function, and a stochastic error term. We propose a procedure to estimate the unknown period and the function values of the periodic component as well as the nonparametric trend function. The theoretical part of the paper establishes the asymptotic properties of our estimators. In particular, we show that our estimator of the period is consistent. In addition, we derive the convergence rates and the limiting distributions of our estimators of the periodic component and the trend function. The asymptotic results are complemented with a simulation study and an application to global temperature anomaly data.

MSC:

62G08	Nonparametric regression and quantile regression
62G20	Asymptotic properties of nonparametric inference
62E20	Asymptotic distribution theory in statistics
65C60	Computational problems in statistics (MSC2010)
62P12	Applications of statistics to environmental and related topics

Keywords:

nonparametric estimation; penalized least squares; temperature anomaly data