Most of the members of this group are from the Statistics Section and Biomaths research group of the Department of Mathematics. Below you can find a list of research areas that members of this group are currently working on and/or would like to work on by applying their developed mathematical and statistical methods.
@article{Nieto-Reyes:2016:10.1214/15-STS532,
author = {Nieto-Reyes, A and Battey, H},
doi = {10.1214/15-STS532},
journal = {Statistical Science},
pages = {61--79},
title = {A topologically valid definition of depth for functional data},
url = {http://dx.doi.org/10.1214/15-STS532},
volume = {31},
year = {2016}
}
TY - JOUR
AB - The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth defining properties is one that addresses the delicate challenge of inherent partial observability of functional data, with fulfillment giving rise to a minimal guarantee on the performance of the empirical depth beyond the idealised and practically infeasible case of full observability. As an incidental product, functional depths satisfying our definition achieve a robustness that is commonly ascribed to depth, despite the absence of a formal guarantee in the multivariate definition of depth. We demonstrate the fulfillment or otherwise of our properties for six widely used functional depth proposals, thereby providing a systematic basis for selection of a depth function.
AU - Nieto-Reyes,A
AU - Battey,H
DO - 10.1214/15-STS532
EP - 79
PY - 2016///
SP - 61
TI - A topologically valid definition of depth for functional data
T2 - Statistical Science
UR - http://dx.doi.org/10.1214/15-STS532
UR - http://hdl.handle.net/10044/1/41332
VL - 31
ER -