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
Assessing the effects of multivariate functional outlier identification and sample robustification on identifying critical PM2.5 air pollution episodes in Medellín, Colombia
TL;DR: In this paper , the effects of robustifying multivariate functional samples on the identification of critical pollution episodes in Medellín, Colombia were investigated. But no clear positive effects of the robustification were identified with the real dataset.
Journal ArticleDOI
Unified statistical inference for a nonlinear dynamic functional/longitudinal data model
TL;DR: In this article , the authors adopt a flexible nonlinear dynamic regression method named the Semi-Varying Coefficient Additive Model (SVAAM), in which the response can be a functional/longitudinal variable, and the explanatory variables can be either a mixture of functional or long-term variables.
Journal ArticleDOI
Test of independence for Hilbertian random variables
Bilol Banerjee,Anil K. Ghosh +1 more
TL;DR: In this paper , a test of independence for functional random variables modelled as elements of Hilbert spaces is proposed, which is based on the d-variable Hilbert-Schmidt Independence Criterion.
Journal ArticleDOI
Functional data analysis for longitudinal data with informative observation times
Caleb Weaver,Luo Xiao,Wenbin Lu +2 more
TL;DR: In this article , the authors show that the covariance function can be estimated appropriately via penalized tensor product splines, both with specific choices of parameters, under a general class of shared random effect models, while a commonly used functional data method may lead to inconsistent model estimation.
Peer Review
Functional proportional hazards mixture cure model and its application to modelling the association between cancer mortality and physical activity in NHANES 2003-2006
TL;DR: In this article , the authors developed a functional proportional hazards mixture cure (FPHMC) model with scalar and functional covariates measured at the baseline and employed the EM algorithm and developed a semiparametric penalized spline-based approach to estimate the dynamic functional coefficients.
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.