Introduction to Functional Data Analysis 1st Edition by Piotr Kokoszka, Matthew Reimherr ISBN 9781498746694 1498746691

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ISBN 10: 1498746691
ISBN 13: 9781498746694
Author: Piotr Kokoszka, Matthew Reimherr

Introduction to Functional Data Analysis 1st Edition Table of contents:

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 analysis of functional data

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

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 xtensions 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

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 unctional 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 problems

11 Random functions

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

References

Index

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Piotr Kokoszka,Matthew Reimherr,Functional,Data Analysis