Adaptive Estimation for Weakly Dependent Functional Times Series
针对弱相依函数型时间序列，提出自适应均值和自协方差函数估计方法，能适应曲线正则性并处理稀疏或密集数据，通过最小化显式二次风险界选择带宽，并推导了均值估计的渐近正态性。
ABSTRACT We propose adaptive mean and autocovariance function estimators for stationary functional time series under ‐approximability assumptions. These estimators are designed to adapt to the regularity of the curves and to accommodate both sparse and dense data designs. The sample paths are observed with error at possibly random design points. Data‐driven local bandwidths are selected by minimizing explicit quadratic risk bounds that exploit the local regularity of the process. As a first step, we introduce a local regularity estimator and derive a nonasymptotic concentration bound for it. We also derive the asymptotic normality of the mean estimator, which allows honest inference for irregular mean functions. Simulations and a real data application illustrate the performance of the new estimators.