Asset Details
Do you wish to reserve the book?
FUNCTIONAL DATA ANALYSIS FOR DENSITY FUNCTIONS BY TRANSFORMATION TO A HILBERT SPACE
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
FUNCTIONAL DATA ANALYSIS FOR DENSITY FUNCTIONS BY TRANSFORMATION TO A HILBERT SPACE
Do you wish to request the book?
FUNCTIONAL DATA ANALYSIS FOR DENSITY FUNCTIONS BY TRANSFORMATION TO A HILBERT SPACE
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
FUNCTIONAL DATA ANALYSIS FOR DENSITY FUNCTIONS BY TRANSFORMATION TO A HILBERT SPACE
2016
Overview
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and, therefore, commonly used Hubert space based methods of functional data analysis are not applicable. To address this problem, we introduce a transformation approach, mapping probability densities to a Hubert space of functions through a continuous and invertible map. Basic methods of functional data analysis, such as the construction of functional modes of variation, functional regression or classification, are then implemented by using representations of the densities in this linear space. Representations of the densities themselves are obtained by applying the inverse map from the linear functional space to the density space. Transformations of interest include log quantile density and log hazard transformations, among others. Rates of convergence are derived for the representations that are obtained for a general class of transformations under certain structural properties. If the subjectspecific densities need to be estimated from data, these rates correspond to the optimal rates of convergence for density estimation. The proposed methods are illustrated through simulations and applications in brain imaging.
Publisher
Institute of Mathematical Statistics,The Institute of Mathematical Statistics
Subject
We currently cannot retrieve any items related to this title. Kindly check back at a later time.