This paper aims to present the various contributions to the Special Issue of the Journal of
Multivariate Analysis on Functional Data Analysis and some related topics including High …

Highest density regions (HDRs) are defined as level sets containing sample points of
relatively high density. Although Euclidean HDR estimation from a random sample …

Anomaly detection is an important problem in many application areas, such as network
security. Many deep learning methods for unsupervised anomaly detection produce good …

Density-based clustering methodology has been widely considered in the statistical
literature for classifying Euclidean observations. However, this approach has not been …

In high-dimensional statistics, the manifold hypothesis presumes that the data lie near low-
dimensional structures, called manifolds. This assumption helps explain why machine …

Regression on manifolds, and, more broadly, statistics on manifolds, has garnered
significant importance in recent years due to the vast number of applications for this type of …

Some recent advances in Set Estimation, from 2009 to the present, are discussed. These
include some new findings, improved convergence rates, and new type of sets under study …

Object oriented data analysis (OODA) can be defined as the statistical analysis of complex
objects. This term comprises any situation where classical inferential techniques are not …

Object oriented data analysis (OODA) can be defined as the statistical analysis of complex
objects. This term, initially introduced by Wang and Marron (2007), encompasses any …

We are most grateful to the five discussants for their enthusiastic response to our review,
insightful comments on various aspects of its content, historical glimpses of the field's …