Nonparametric estimation of a periodic sequence in the presence of a smooth trend
提出一种非参数回归方法，同时估计未知周期、周期分量和平滑趋势函数，并证明周期估计的一致性及收敛速度，适用于全球温度异常数据分析。
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.