Robust Linear Interpolation and Extrapolation of Stationary Time Series in Lp
Robust Linear Interpolation and Extrapolation of Stationary Time Series in Lp
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Lp 中平稳时间序列的鲁棒线性插值和外推
DOI：
10.1111/jtsa.12502
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发表时间：
2019
影响因子：
0.9
通讯作者：
Taniguchi Masanobu
中科院分区：
文献类型：
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作者：
Liu Yan;Xue Yujie;Taniguchi Masanobu
为了处理谱分布的不确定性，我们考虑了平稳过程在Lp中的Minimax插值和外推问题。内插和外插问题可以看作是复平面上单位圆盘上的线性逼近问题。虽然鲁棒一步前预报器和稳健外推器在以往的文献中已经被单独考虑，但我们从观测集的角度和Lp范数下内插外推误差的评估角度，给出了一般框架下不确定类求极小极大外推器和极小极大外推器的两个条件.我们证明了在我们的条件下，对于被未知谱密度污染的谱密度类ε-，存在极大极小算子和外推算子。当不确定类中含有对Lebesgue测度不绝对连续的谱分布函数时，证明了在Lp中存在一个近似的内插外推算子，使得当谱分布具有密度时，其最大内插外推误差任意接近于极小极大误差.我们的结果适用于平稳可调和稳定过程。
To deal with uncertainty of the spectral distribution, we consider minimax interpolation and extrapolation problems inLpfor stationary processes. The interpolation and extrapolation problems can be regarded as a linear approximation problem on the unit disk in the complex plane. Although the robust one‐step‐ahead predictor and interpolator has already been considered separately in the previous literature, we give two conditions for the uncertainty class to find the minimax interpolator and extrapolator in the general framework from both the point of view of the observation set and the point of view of evaluation on the interpolation and extrapolation error under theLp‐norm. We show that there exists a minimax interpolator and extrapolator for the class of spectral densitiesε‐contaminated by unknown spectral densities under our conditions. When the uncertainty class contains spectral distribution functions which are not absolutely continuous to the Lebesgue measure, we show that there exists an approximate interpolator and extrapolator inLpsuch that its maximal interpolation and extrapolation error is arbitrarily close to the minimax error when the spectral distributions have densities. Our results are applicable to the stationary harmonizable stable processes.