Introduction: Examples of Functional Data

Wavelet-based functional data analysis (FDA) is a modern approach to dealing with statistical inference when observations are curves or images. Making inference (estimation and testing) in the wavelet domain is beneficial in several respects such as: reduction of dimensionality, decorrelation, localization, and regularization. This chapter gives an overview of theory for wavelet-based functional analysis, reviews relevant references, and provides some examples that will be used in the next chapters.

[1]  Spencer Graves,et al.  Functional Data Analysis with R and MATLAB , 2009 .

[2]  Violaine Cahouët,et al.  Static optimal estimation of joint accelerations for inverse dynamics problem solution. , 2002, Journal of biomechanics.

[3]  João Ricardo Sato,et al.  A method to produce evolving functional connectivity maps during the course of an fMRI experiment using wavelet-based time-varying Granger causality , 2006, NeuroImage.

[4]  Henry W. Altland,et al.  Applied Functional Data Analysis , 2003, Technometrics.

[5]  João Ricardo Sato,et al.  Wavelet based time-varying vector autoregressive modelling , 2007, Comput. Stat. Data Anal..

[6]  M. Dewhirst,et al.  Variability in blood flow and pO2 in tumors in response to carbogen breathing. , 1998, International journal of radiation oncology, biology, physics.

[7]  Jianqing Fan.  Test of Significance Based on Wavelet Thresholding and Neyman's Truncation , 1996 .

[8]  M. Dewhirst,et al.  Temporal changes in PO2 of R3230AC tumors in Fischer-344 rats. , 1998, International journal of radiation oncology, biology, physics.

[9]  Bruce I. Turetsky,et al.  Wavelet ANOVA and fMRI , 1999, Optics & Photonics.

[10]  J. Rice,et al.  Smoothing spline models for the analysis of nested and crossed samples of curves , 1998 .

[11]  P. Müller,et al.  A Bayesian Model for Detecting Acute Change in Nonlinear Profiles , 2001 .

[12]  Frédéric Ferraty,et al.  Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics) , 2006 .

[13]  J Bruce German,et al.  Genomics and metabolomics as markers for the interaction of diet and health: lessons from lipids. , 2003, The Journal of nutrition.

[14]  T. Fearn,et al.  Bayesian Wavelet Regression on Curves With Application to a Spectroscopic Calibration Problem , 2001 .

[15]  Luiz A Baccalá,et al.  Frequency domain connectivity identification: An application of partial directed coherence in fMRI , 2009, Human brain mapping.

[16]  F. Ferraty,et al.  The Oxford Handbook of Functional Data Analysis , 2011, Oxford Handbooks Online.

[17]  D E Bauman,et al.  Metabolomics in the opening decade of the 21st century: building the roads to individualized health. , 2004, The Journal of nutrition.

[18]  Piotr Kokoszka,et al.  Inference for Functional Data with Applications , 2012 .