{"product_id":"theoretical-foundations-of-functional-data-analysis-with-an-introduction-to-linear-operators-hardcover","title":"Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators - Hardcover","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eTailen Hsing\u003c\/b\u003e (Author), \u003cb\u003eRandall Eubank\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003eTheoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators\u003c\/i\u003e provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA).\u003cbr\u003e\u003cbr\u003eThe self-contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self-adjoint and non self-adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis.\u003cbr\u003e\u003cbr\u003eThis book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eProvides essential coverage of functional data analysis and related areas.\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003eThis book provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA).\u003cbr\u003e\u003cbr\u003eThe self-contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self-adjoint and non self-adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis.\u003cbr\u003e\u003cbr\u003e\u003ci\u003eKey features\u003c\/i\u003e \u003cbr\u003e\u003cbr\u003e\u003c\/p\u003e \u003cul\u003e \u003cli\u003eProvides a concise but rigorous account of the theoretical background of FDA\u003c\/li\u003e \u003cli\u003eIntroduces topics in various areas of mathematics, probability and statistics from the perspective of FDA\u003c\/li\u003e \u003cli\u003ePresents a systematic exposition of the fundamental statistical issues in FDA\u003c\/li\u003e \u003cli\u003eDevelops all material from first principles, assuming no prior knowledge of linear operator or FDA\u003c\/li\u003e \u003c\/ul\u003e \u003cbr\u003eThis book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003cb\u003eTailen Hsing\u003c\/b\u003e Professor, Department of Statistics, University of Michigan, USA. Professor Hsing is a fellow of International Statistical Institute and of the Institute of Mathematical Statistics. He has published numerous papers on subjects ranging from bioinformatics to extreme value theory, functional data analysis, large sample theory and processes with long memory.\u003cb\u003e\u003cbr\u003e \u003cbr\u003e \u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\u003cb\u003eRandall Eubank\u003c\/b\u003e Professor Emeritus, School of Mathematical and Statistical Sciences, Arizona State University, USA. Professor Eubank is well know and respected in the functional data analysis (FDA) field. He has published numerous papers on the subject and is a regular invited speaker at key meetings.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 368\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.9 x 9 x 6 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e May 06, 2015\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":45342569431142,"sku":"9780470016916","price":162.68,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0599\/7255\/0758\/files\/Z2I2ZElZSnp6U1NrdXZSNDkyVEd5UT09.webp?v=1774889404","url":"https:\/\/infinitylightwa.com\/products\/theoretical-foundations-of-functional-data-analysis-with-an-introduction-to-linear-operators-hardcover","provider":"Infinity Light","version":"1.0","type":"link"}