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Introduction to Functional Data Analysis provides a concise
textbook introduction to the field. It explains how to analyze
functional data, both at exploratory and inferential levels. It
also provides a systematic and accessible exposition of the
methodology and the required mathematical framework. The book can
be used as textbook for a semester-long course on FDA for advanced
undergraduate or MS statistics majors, as well as for MS and PhD
students in other disciplines, including applied mathematics,
environmental science, public health, medical research, geophysical
sciences and economics. It can also be used for self-study and as a
reference for researchers in those fields who wish to acquire solid
understanding of FDA methodology and practical guidance for its
implementation. Each chapter contains plentiful examples of
relevant R code and theoretical and data analytic problems. The
material of the book can be roughly divided into four parts of
approximately equal length: 1) basic concepts and techniques of
FDA, 2) functional regression models, 3) sparse and dependent
functional data, and 4) introduction to the Hilbert space framework
of FDA. The book assumes advanced undergraduate background in
calculus, linear algebra, distributional probability theory,
foundations of statistical inference, and some familiarity with R
programming. Other required statistics background is provided in
scalar settings before the related functional concepts are
developed. Most chapters end with references to more advanced
research for those who wish to gain a more in-depth understanding
of a specific topic.
This book presents recently developed statistical methods and
theory required for the application of the tools of functional data
analysis to problems arising in geosciences, finance, economics and
biology. It is concerned with inference based on second order
statistics, especially those related to the functional principal
component analysis. While it covers inference for independent and
identically distributed functional data, its distinguishing feature
is an in depth coverage of dependent functional data structures,
including functional time series and spatially indexed functions.
Specific inferential problems studied include two sample inference,
change point analysis, tests for dependence in data and model
residuals and functional prediction. All procedures are described
algorithmically, illustrated on simulated and real data sets, and
supported by a complete asymptotic theory. The book can be read at
two levels. Readers interested primarily in methodology will find
detailed descriptions of the methods and examples of their
application. Researchers interested also in mathematical
foundations will find carefully developed theory. The organization
of the chapters makes it easy for the reader to choose an
appropriate focus. The book introduces the requisite, and
frequently used, Hilbert space formalism in a systematic manner.
This will be useful to graduate or advanced undergraduate students
seeking a self-contained introduction to the subject. Advanced
researchers will find novel asymptotic arguments.
This book presents recently developed statistical methods and
theory required for the application of the tools of functional data
analysis to problems arising in geosciences, finance, economics and
biology. It is concerned with inference based on second order
statistics, especially those related to the functional principal
component analysis. While it covers inference for independent and
identically distributed functional data, its distinguishing feature
is an in depth coverage of dependent functional data structures,
including functional time series and spatially indexed functions.
Specific inferential problems studied include two sample inference,
change point analysis, tests for dependence in data and model
residuals and functional prediction. All procedures are described
algorithmically, illustrated on simulated and real data sets, and
supported by a complete asymptotic theory. The book can be read at
two levels. Readers interested primarily in methodology will find
detailed descriptions of the methods and examples of their
application. Researchers interested also in mathematical
foundations will find carefully developed theory. The organization
of the chapters makes it easy for the reader to choose an
appropriate focus. The book introduces the requisite, and
frequently used, Hilbert space formalism in a systematic manner.
This will be useful to graduate or advanced undergraduate students
seeking a self-contained introduction to the subject. Advanced
researchers will find novel asymptotic arguments.
Introduction to Functional Data Analysis provides a concise
textbook introduction to the field. It explains how to analyze
functional data, both at exploratory and inferential levels. It
also provides a systematic and accessible exposition of the
methodology and the required mathematical framework. The book can
be used as textbook for a semester-long course on FDA for advanced
undergraduate or MS statistics majors, as well as for MS and PhD
students in other disciplines, including applied mathematics,
environmental science, public health, medical research, geophysical
sciences and economics. It can also be used for self-study and as a
reference for researchers in those fields who wish to acquire solid
understanding of FDA methodology and practical guidance for its
implementation. Each chapter contains plentiful examples of
relevant R code and theoretical and data analytic problems. The
material of the book can be roughly divided into four parts of
approximately equal length: 1) basic concepts and techniques of
FDA, 2) functional regression models, 3) sparse and dependent
functional data, and 4) introduction to the Hilbert space framework
of FDA. The book assumes advanced undergraduate background in
calculus, linear algebra, distributional probability theory,
foundations of statistical inference, and some familiarity with R
programming. Other required statistics background is provided in
scalar settings before the related functional concepts are
developed. Most chapters end with references to more advanced
research for those who wish to gain a more in-depth understanding
of a specific topic.
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