Introduction to functional data analysis /

Bibliographic Details
Main Authors:	Kokoszka, P. (Piotr) (Author), Reimherr, Matthew (Author)
Corporate Author:	ProQuest (Firm)
Format:	eBook
Language:	English
Published:	Boca Raton, FL : CRC Press, [2017]
Series:	Texts in statistical science.
Subjects:	Functional analysis. Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

Machine generated contents note: 1.First steps in the analysis of functional data
1.1.Basis expansions
1.2.Sample mean and covariance
1.3.Principal component functions
1.4.Analysis of BOA stock returns
1.5.Diffusion tensor imaging
1.6.Chapter 1 problems
2.Further topics in exploratory FDA
2.1.Derivatives
2.2.Penalized smoothing
2.3.Curve alignment
2.4.Further reading
2.5.Chapter 2 problems
3.Mathematical framework for functional data
3.1.Square integrable functions
3.2.Random functions
3.3.Linear transformations
4.Scalar
on
function regression
4.1.Examples
4.2.Review of standard regression theory
4.3.Difficulties specific to functional regression
4.4.Estimation through a basis expansion
4.5.Estimation with a roughness penalty
4.6.Regression on functional principal components
4.7.Implementation in the refund package
4.8.Nonlinear scalar
on
function regression
4.9.Chapter 4 problems
Note continued: 5.Functional response models
5.1.Least squares estimation and application to angular motion
5.2.Penalized least squares estimation
5.3.Functional regressors
5.4.Penalized estimation in the refund package
5.5.Estimation based on functional principal components
5.6.Test of no effect
5.7.Verification of the validity of a functional linear model
5.8.Extensions and further reading
5.9.Chapter 5 Problems
6.Functional generalized linear models
6.1.Background
6.2.Scalar-on-function GLM's
6.3.Functional response GLM
6.4.Implementation in the refund package
6.5.Application to DTI
6.6.Further reading
6.7.Chapter 6 problems
7.Sparse FDA
7.1.Introduction
7.2.Mean function estimation
7.3.Covariance function estimation
7.4.Sparse functional PCA
7.5.Sparse functional regression
7.6.Chapter 7 problems
8.Functional time series
8.1.Fundamental concepts of time series analysis
Note continued: 8.2.Functional autoregressive process
8.3.Forecasting with the Hyndman
Ullah method
8.4.Forecasting with multivariate predictors
8.5.Long-run covariance function
8.6.Testing stationarity of functional time series
8.7.Generation and estimation of the FAR(1) model using package fda
8.8.Conditions for the existence of the FAR(1) process
8.9.Further reading and other topics
8.10.Chapter 8 problems
9.Spatial functional data and models
9.1.Fundamental concepts of spatial statistics
9.2.Functional spatial fields
9.3.Functional kriging
9.4.Mean function estimation
9.5.Implementation in the R package geofd
9.6.Other topics and further reading
9.7.Chapter 9 problems
10.Elements of Hilbert space theory
10.1.Hilbert space
10.2.Projections and orthonormal sets
10.3.Linear operators
10.4.Basics of spectral theory
10.5.Tensors
10.6.Chapter 10 problems
11.Random functions
Note continued: 11.1.Random elements in metric spaces
11.2.Expectation and covariance in a Hilbert space
11.3.Gaussian functions and limit theorems
11.4.Functional principal components
11.5.Chapter 11 problems
12.Inference from a random sample
12.1.Consistency of sample mean and covariance functions
12.2.Estimated functional principal components
12.3.Asymptotic normality
12.4.Hypothesis testing about the mean
12.5.Confidence bands for the mean
12.6.Application to BOA cumulative returns
12.7.Proof of Theorem 12.2.1
12.8.Chapter 12 problems.