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Stochastic Inverse Regression and Reproducing Kernel Hilbert Space
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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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