Ebook: 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.

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KEY BENEFIT: For over 30 years, this text has provided students with the information they need to understand and apply multivariate data analysis. Hair, et. al provides an applications-oriented introduction to multivariate analysis for the non-statistician. By reducing heavy statistical research into fundamental concepts, the text explains to students how to understand and make use of the results of specific statistical techniques. In this seventh revision, the organization of the chapters has been greatly simplified. New chapters have been added on structural equations modeling, and all sections have been updated to reflect advances in technology, capability, and mathematical techniques. Preparing For a MV Analysis; Dependence Techniques; Interdependence Techniques; Moving Beyond the Basic Techniques MARKET:  Statistics and statistical research can provide managers with invaluable data. This textbook teaches them the different kinds of analysis that can be done and how to apply the techniques in the workplace Part 1. Independent functional observations -- Hilbert space model for functional data -- Functional principal components -- Canonical correlation analysis -- Two sample inference for the mean and covariance functions -- Detection of changes in the mean function -- Portmanteau test of independence -- Functional data structures -- Part 2. The functional linear model -- Functional linear models -- Test for lack of effect in the functional linear model -- Two sample inference for regression kernels -- Tests for error correlation in the functional linear model -- A test of significance in functional quadratic regression -- Part 3. Dependent functional data -- Functional autoregressive model -- Change point detection in the functional autoregressive process -- Determining the order of the functional autoregressive model -- Functional time series -- Spatially distributed functional data -- Consistency of the simple mean and the empirical functional principal components for spatially distributed curves