Functional data analysis is ubiquitous in most areas of sciences and engineering. Several paradigms are proposed to deal with the dimensionality problem which is inherent to this type of data. Sparseness, penalization, thresholding, among other principles, have been used to tackle this issue. We discuss here a solution based on a finite-dimensional functional space. We employ wavelet representation of the functionals to estimate this finite dimension, and successfully model a time series of curves. The proposed method is shown to have nice asymptotic properties. Moreover, the wavelet representation permits the use of several bootstrap procedures, and it results in faster computing algorithms. Besides the theoretical and computational properties, some simulation studies and an application to real data are provided.

中文翻译：

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曲线时间序列维数的小波估计

功能数据分析在大多数科学和工程领域无处不在。提出了几种范式来处理此类数据固有的维数问题。稀疏、惩罚、阈值等原则已被用来解决这个问题。我们在这里讨论基于有限维函数空间的解决方案。我们使用泛函的小波表示来估计这个有限维度，并成功地对曲线的时间序列进行建模。所提出的方法被证明具有很好的渐近特性。此外，小波表示允许使用多个引导程序，并导致更快的计算算法。除了理论和计算特性外，还提供了一些模拟研究和对实际数据的应用。