RT Journal Article
T1 Statistical properties of partially observed integrated functional depths
A1 Elías Fernández, Antonio
A1 Nagy, Stanislav
K1 Estadística
AB Integrated functional depths (IFDs) present a versatile toolbox of methods introducing notions of ordering, quantiles, and rankings into a functional data analysis context. They provide fundamental tools for nonparametric inference of infinite-dimensional data. Recently, the literature has extended IFDs to address the challenges posed by partial observability of functional data, commonly encountered in practice. That resulted in the development of partially observed integrated functional depths (POIFDs). POIFDs have demonstrated good empirical results in simulated experiments and real problems. However, there are still no theoretical results in line with the state of the art of IFDs. This article addresses this gap by providing theoretical support for POIFDs, including (i) uniform consistency of their sample versions, (ii) weak continuity with respect to the underlying probability measure, and (iii) uniform consistency for discretely observed functional data. Finally, we present a sensitivity analysis that evaluates how our theoretical results are affected by violations of the main assumptions.
PB Springer
YR 2024
FD 2024
LK https://hdl.handle.net/10630/35290
UL https://hdl.handle.net/10630/35290
LA eng
NO Elías, A., Nagy, S. Statistical properties of partially observed integrated functional depths. TEST (2024). https://doi.org/10.1007/s11749-024-00954-6
NO Funding for open access publishing: Universidad Málaga/CBUA.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026