Principal points and elliptical distributions from the multivariate setting to the functional case

Robust smoothed canonical correlation analysis for functional data

“…Assume that (X, Y ) ⊤ ∼ E(µ, Γ, ϕ) where E(µ, Γ, ϕ) denotes an elliptical distribution, as defined in Bali and Boente (2009), with parameters µ = (µ 1 , µ 2 ) ⊤ ∈ H × H and Γ is as in (4.8). As a consequence of the definition of elliptical random elements, for any u,…”

Optimal estimators of principal points for minimizing expected mean squared distance

“…For reference to the allometric extension model, see, for example, Bartoletti et al (1999), Tarpey and Ivey (2006), Kurata et al (2008). Although the definition of principal points is given in terms of Euclidean spaces, the extension to random functions (on Hilbert spaces) has been given and discussed (e.g., Tarpey and Kinateder, 2003;Mizuta, 2007, 2008;Bali and Boente, 2009). Recently, Ruwet and Haesbroeck (2013) discussed the classification efficiency of 2-principal points.…”

Comparison of model selection methods for the estimation of principal points for a multivariate binary distribution

“…In fact, principal points are applied to various problems, including product design and quality control problems, such as finding an optimal set of designs for masks (Flury, 1993), selective assembly for two parts in the manufacturing field (Mease et al, 2004;Mease and Nair, 2006;Matsuura, 2011), functional data analysis (Tarpey and Kinateder, 2003;Shimizu and Mizuta, 2007;Shimizu and Mizuta, 2008), and classification analysis of the placebo effect (Tarpey, et al, 2010). The properties of principal points have been widely studied in the literature (e.g., Tarpey and Flury, 1995;Zoppè, 1995;Yamamoto and Shinozaki, 2000;Gu and Mathew, 2001;Kurata, 2008;Bali and Boente, 2009;Matsuura and Kurata, 2011;Matsuura and Kurata, 2014), and the parametric estimation of principal points of some continuous distributions has also been discussed (e.g., Flury, 1993;Tarpey, 1997;Stampfer and Stadlober, 2002;Tarpey, 2007).…”