# Multidimensional Data Analysis

##### Citations

1,102 citations

^{1}

197 citations

### Cites background from "Multidimensional Data Analysis"

...It is also possible to define a generalized cross-validation (GCV) criterion (Craven and Wahba, 1979) which consists in substituting each element Pik,ik by its average value, i....

[...]

...As explained in the introduction, in a linear smoothing framework, the prediction error for an individual i can be written explicitly from the adjustment error and the smoothing matrix (Craven and Wahba, 1979) as (3). Consequently, there is no need to perform cross-validation to compute the mean square error of prediction. It is sufficient to compute the adjusted vector and the smoothing matrix. A linear smoother means that the fit at a point can be expressed as a linear combination of the response vector and that the coefficients in the linear combination do not depend on the response vector. In other words, ŷ = Py with P independent of y. The smoother involved in PCA (9) is nonlinear since it depends on the data. In the framework of nonlinear smoothers, only approximations of the prediction error can be derived as shown in O’Sullivan and Wahba (1985), Ke and Wang (2004) and Sima (2006, p....

[...]

...It is also possible to define a generalized cross-validation (GCV) criterion (Craven and Wahba, 1979) which consists in substituting each element Pik,ik by its average value, i.e. tr(P)/(IK)....

[...]

...As explained in the introduction, in a linear smoothing framework, the prediction error for an individual i can be written explicitly from the adjustment error and the smoothing matrix (Craven and Wahba, 1979) as (3)....

[...]

194 citations

164 citations

162 citations