Stochastic Inverse Regression and Reproducing Kernel Hilbert Space: with Applications in Functional Data Analysis

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Press: VDM Verlag (July 9, 2009)
ISBN:9783639177923
Author Name:Ren, Haobo
Pages:112
Language:English

Content

The basic philosophy of Functional Data Analysis   (FDA) is to think of the observed data functions as   elements of a possibly infinite-dimensional function   space. 
Most of the current research topics on FDA focus on advancing theoretical tools and extending existing multivariate techniques to accommodate the infinite-dimensional nature of data.
This monograph reports contributions on both fronts, where a unifying inverse regression theory for both the multivariate setting and functional data from a Reproducing Kernel Hilbert Space (RKHS) prospective is developed.
We proposed a stochastic multiple-index model, two RKHS-related inverse regression procedures, a ``slicing'' approach and a kernel approach, as well as an asymptotic theory were introduced to the statistical framework.
Some general computational issues of FDA were discussed, Some general computational issues of FDA were discussed, which led to smoothed versions of the stochastic inverse regression methods.

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Textbooks,Science & Mathematics,Mathematics,Statistics,Science & Math,Applied,Probability & Statistics



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