论文标题
功能数据分析的本地化过程
Localization processes for functional data analysis
论文作者
论文摘要
我们为功能数据提出了$ k $ neart邻居的替代方案，在该功能数据中，近似相邻曲线是由功能样本构建的分段函数。使用满足稳定标准的局部定义距离函数，当数据曲线的数量足够大时，我们可以点上和全局近似会导致功能空间。当在I.I.D给出的时间点上观察到有限数量的曲线时，我们利用此特征来发展渐近理论。基数增加到无穷大的样本。我们使用这些结果来研究估计部分观察到的功能数据样本未观察到的段的问题，以及研究功能分类和离群检测的问题。对于此类问题，我们的方法与该领域的基准预测具有竞争力，有时还优于该方法。
We propose an alternative to $k$-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies stabilization criteria, we establish pointwise and global approximation results in function spaces when the number of data curves is large enough. We exploit this feature to develop the asymptotic theory when a finite number of curves is observed at time-points given by an i.i.d. sample whose cardinality increases up to infinity. We use these results to investigate the problem of estimating unobserved segments of a partially observed functional data sample as well as to study the problem of functional classification and outlier detection. For such problems, our methods are competitive with and sometimes superior to benchmark predictions in the field.
