标题： 小波估计曲线时间序列的维数 显示英文标题

标题： Wavelet estimation of the dimensionality of curve time series

摘要： 函数数据分析在科学和工程的各个领域无处不在。为了解决这种数据固有的高维问题，提出了几种范式。稀疏性、惩罚、阈值化等原则已被用于解决这一问题。本文讨论了一种基于有限维函数空间的解决方案。我们利用泛函的小波表示来估计这个有限维，并成功地对曲线的时间序列进行建模。所提出的方法显示出良好的渐近性质。此外，小波表示允许使用多种自助程序，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一个实际数据的应用。 显示英文摘要

摘要： 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.