Functional analysis of variance for Hilbert-valued multivariate fixed effect models |
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Authors: | MD Ruiz-Medina |
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Institution: | Department of Statistics and O.R., Faculty of Sciences, University of Granada, Granada, Spain |
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Abstract: | This paper presents new results on functional analysis of variance for fixed effect models with correlated Hilbert-valued Gaussian error components. The geometry of the reproducing kernel Hilbert space of the error term is considered in the computation of the total sum of squares, the residual sum of squares, and the sum of squares due to the regression. Under suitable linear transformation of the correlated functional data, the distributional characteristics of these statistics, their moment generating and characteristic functions, are derived. Fixed effect linear hypothesis testing is finally formulated in the Hilbert-valued multivariate Gaussian context considered. |
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Keywords: | fixed effect model Gaussian measure on a separable Hilbert space Hilbert-valued Gaussian random vector linear hypothesis testing reproducing kernel Hilbert space |
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