Peter Hall, functional data analysis and random objects

Properties of Principal Component Methods for Functional and Longitudinal Data Analysis by Peter Hall,

The use of principal component methods to analyze functional data is appropriate in a wide range of different settings. In studies of “functional data analysis,” it has often been assumed that a sample of random functions is observed precisely, in the continuum and without noise. While this has been the traditional setting for functional data analysis, in the context of longitudinal data analys...

Peter Hall ’ S Work on High - Dimensional Data and Classification

In this article, I summarise Peter Hall’s contributions to high-dimensional data, including their geometric representations and variable selection methods based on ranking. I also discuss his work on classification problems, concluding with some personal reflections on my own interactions with him. This article complements [Ann. Statist. 44 (2016) 1821–1836; Ann. Statist. 44 (2016) 1837–1853; A...

Functional Data Analysis of Tree Data Objects.

Data analysis on non-Euclidean spaces, such as tree spaces, can be challenging. The main contribution of this paper is establishment of a connection between tree data spaces and the well developed area of Functional Data Analysis (FDA), where the data objects are curves. This connection comes through two tree representation approaches, the Dyck path representation and the branch length represen...

Functional Data Analysis of Populations of Tree-structured Objects

Nonparametric Estimation When Data on Derivatives Are Available by Peter Hall

We consider settings where data are available on a nonparametric function and various partial derivatives. Such circumstances arise in practice, for example in the joint estimation of cost and input functions in economics. We show that when derivative data are available, local averages can be replaced in certain dimensions by nonlocal averages, thus reducing the nonparametric dimension of the p...