A polynomial spline estimator is proposed for the mean function of dense functional data together with a simultaneous confidence band which is asymptotically correct. In addition, the spline estimator and its accompanying confidence band enjoy oracle efficiency in the sense that they are asymptotically the same as if all random trajectories are observed entirely and without errors. The confidence band is also extended to the difference of mean functions of two populations of functional data. Simulation experiments provide strong evidence that corroborates the asymptotic theory while computing is efficient. The confidence band procedure is illustrated by analysing the near-infrared spectroscopy data.

中文翻译：

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基于密集函数数据的均值函数的同时推断

为密集函数数据的平均函数以及渐近正确的同时置信带提出了多项式样条估计器。此外，样条估计器及其随附的置信带享有预言机效率，因为它们渐近相同，就好像所有随机轨迹都被完全观察到且没有错误一样。置信带还扩展到两个函数数据群的平均函数的差异。仿真实验提供了有力的证据，证实了渐近理论，同时计算是有效的。通过分析近红外光谱数据来说明置信带过程。