Functional Data Analysis
TLDR
In this article, the authors provide an overview of FDA, starting with simple statistical notions such as mean and covariance functions, then covering some core techniques, the most popular of which is functional principal component analysis (FPCA).Abstract:
With the advance of modern technology, more and more data are being recorded continuously during a time interval or intermittently at several discrete time points. These are both examples of functional data, which has become a commonly encountered type of data. Functional data analysis (FDA) encompasses the statistical methodology for such data. Broadly interpreted, FDA deals with the analysis and theory of data that are in the form of functions. This paper provides an overview of FDA, starting with simple statistical notions such as mean and covariance functions, then covering some core techniques, the most popular of which is functional principal component analysis (FPCA). FPCA is an important dimension reduction tool, and in sparse data situations it can be used to impute functional data that are sparsely observed. Other dimension reduction approaches are also discussed. In addition, we review another core technique, functional linear regression, as well as clustering and classification of functional d...read more
Citations
More filters
Journal ArticleDOI
Change point detection for the intraday volatility using functional ARCH and conditional Copula
Jong Min Kim,S.Y. Hwang +1 more
TL;DR: In this article , a conditional-copula multiple change point detection (CPD) method for intraday volatilities is proposed using fARCH(1), bivariate Gaussian Copula and t-Copula conditional distributions.
Posted Content
Are Multilevel functional models the next step in sports biomechanics and wearable technology? A case study of Knee Biomechanics patterns in typical training sessions of recreational runners
TL;DR: In this article, a multilevel functional model was proposed to detect and characterize biomechanical changes along different sport training sessions, focusing on the relevant cases to identify differences in knee biomechanics in recreational runners during low and high-intensity exercise sessions.
Journal ArticleDOI
Coupling sparse Cox models with clustering of longitudinal transcriptomics data for trauma prognosis
TL;DR: In this article, a multivariate time series (MTS) clustering was applied to analyze gene expression over time and to stratify patients with similar trajectories, which revealed a strong relationship between gene expression trajectory and patients' recovery.
Journal ArticleDOI
Partially linear functional quantile regression in a reproducing kernel Hilbert space
TL;DR: In this paper , the authors considered quantile functional regression with a functional part and a scalar linear part and established the optimal prediction rate for the model under mild assumptions in the reproducing kernel Hilbert space (RKHS) framework.
Novel specification tests for additive concurrent model formulation based on martingale difference divergence
TL;DR: New tests to measure the conditional mean independence in the concurrent model framework taking under consideration all observed time instants are proposed, including global dependence tests to quantify the effect of a group of covariates in the response as well as partial ones to apply covariates selection.
References
More filters
Journal ArticleDOI
Nonlinear dimensionality reduction by locally linear embedding.
Sam T. Roweis,Lawrence K. Saul +1 more
TL;DR: Locally linear embedding (LLE) is introduced, an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs that learns the global structure of nonlinear manifolds.
Journal ArticleDOI
A global geometric framework for nonlinear dimensionality reduction.
TL;DR: An approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set and efficiently computes a globally optimal solution, and is guaranteed to converge asymptotically to the true structure.
Journal ArticleDOI
Dynamic programming algorithm optimization for spoken word recognition
TL;DR: This paper reports on an optimum dynamic progxamming (DP) based time-normalization algorithm for spoken word recognition, in which the warping function slope is restricted so as to improve discrimination between words in different categories.
Journal ArticleDOI
Generalized Additive Models
Trevor Hastie,Robert Tibshirani +1 more
TL;DR: The class of generalized additive models is introduced, which replaces the linear form E fjXj by a sum of smooth functions E sj(Xj), and has the advantage of being completely auto- matic, i.e., no "detective work" is needed on the part of the statistician.