Inference for Functional Data with Applications

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.

• Asymptotic theory
• Distributed functions
• Functional data analysis
• Functional time series
• Hilbert space theory
• Regression model

From the reviews:

"This is an attractive, impressive and useful book, which gives an effective account of statistical methods and theory used in functional data analysis, as applied to problems arising in many fields, including finance, biological sciences, physics, the geosciences and economics. It serves as an excellent, contemporary reference text. Functional data analysis concerns statistical inference when individual observations take the form of functions defined over some set, perhaps representing time or spatial location...Functional data analysis is a very broad, active research area. I believe that the authors succeed in their basic aim of speaking both to readers interested in methodology, who will find detailed descriptions of inferential procedures (based around the use of R) and evidence of their usefulness, and also to researchers interested in the underlying mathematics, which is presented cleanly, without too much technical fuss. It is very readable, and would provide an excellent basis for advanced study, at the graduate level, of this important and active area of statistics." (G. Alastair Young, International Statistical Review, 82, 1, 2014)

“This book offers an up-to-date perspective on the booming field of statistics with functional data [often called Functional Data Analysis (FDA)]. … this book is a timely, valuable addition to the current textbooks on FDA. It will surely find its place among the well-known references … .” (Antonio Cuevas, Mathematical Reviews, January, 2013)

• Department of Mathematics, University of Utah, Salt Lake City, USA

  Lajos Horváth

• Department of Statistics, Colorado State University, Fort Collins, USA

  Piotr Kokoszka

Lajos Horváth is Professor of Mathematics at the University of Utah. He has served on the editorial boards of Statistics & Probability Letters, Journal of Statistical Planning and Inference and Journal of Time Series Econometrics. He has coauthored more than 250 research papers and 3 books, including Weighted Approximations in Probability and Statistics and Limit Theorems in Change-Point Analysis (both with Miklós Csörgö).

Piotr Kokoszka is Professor of Statistics at Colorado State University. He has served on the editorial boards of the journals Statistical Modelling and Computational Statistics. He has coauthored over 100 papers in areas of statistics and its applications focusing on dependent data.