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Methodology and theory for partial least squares applied to functional data. (English) Zbl 1246.62084

Summary: The partial least squares procedure was originally developed to estimate the slope parameter in multivariate parametric models. More recently it has gained popularity in the functional data literature. There, the partial least squares estimator of the slope is either used to construct linear predictive models, or as a tool to project the data onto a one-dimensional quantity that is employed for further statistical analysis. Although the partial least squares approach is often viewed as an attractive alternative to projections onto the principal component basis, its properties are less well known than those of the latter, mainly because of its iterative nature. We develop an explicit formulation of partial least squares for functional data, which leads to insightful results and motivates new theory, demonstrating consistency and establishing convergence rates.

MSC:

62G05 Nonparametric estimation
62G08 Nonparametric regression and quantile regression
62H25 Factor analysis and principal components; correspondence analysis
62G20 Asymptotic properties of nonparametric inference
65C60 Computational problems in statistics (MSC2010)

Software:

ElemStatLearn

References:

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