2020/07/31 by Antonio Elías, Raúl Jiménez, Elías, Antonio +3
Computer Science · Mathematics · #Anomaly Detection Techniques and Applications #Applications (stat.AP) #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2007.16059
openalex publication_date 2020/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.