fda.usc (version 0.9.4)

fregre.pc.cv: Functional Regression using selection of number of principal components

Description

Functional Regression with scalar response using selection of number of principal components through cross-validation. The algoritm selects the principal components with best estimates the response. The select is performed by cross-validation (CV) or Model Selecttion Criteria (MSC). After is computing functional regression using the best selection of Principal Components.

Usage

fregre.pc.cv(fdataobj,y,kmax=8,criteria="SIC",...)

Arguments

fdataobj

fdata class object.

y

Scalar response with length n.

kmax

Maximum number of principal comoponents.

criteria

Type of cross-validation (CV) or Model Selecttion Criteria (MSC) applied. Possible values are "CV", "AIC", "AICc", "SIC".

...

Further arguments passed to fregre.pc

Value

• Return:
• pc.opt
  Index of principal comoponents selected.
• MSC.min
  Minimum Model Selecttion Criteria (MSC) value for pc.opt principal components.
• pc.order
  Complete sequence of principal components selected in each iteration.
• MSC
  Complete sequence of minimum Model Selecttion Criteria (MSC) value for pc.opt principal components in each iteration.
• fregre.pc
  object for pc.opt principal components.

Details

The algorithm for selecting the best principal components from the first kmax is: 1.-Calculate the best principal component (pc.order[1]) between kmax first. 2.-Calculate the second-best principal component (pc.order [2]) between the (kmax-1) and calculate the criteria value of the two principal components. 3.-The process (point 1 and 2) is repeated until kmax principal component (pc.order[kmax]). The method select the principal components (pc.opt=pc.order[1:k.min]) with minimum MSC criteria. 4.-Finally, is computing functional regression between functional explanatory variable and scalar response using the best selection of Principal Components, for more details see fregre.pc.

References

Cai T., Hall P. 2006. Prediction in functional linear regression. Annals of Statistics 34: 2159{-}2179. Cardot H, Ferraty F, Sarda P. 1999. Functional linear model. Statistics and Probability Letters 45: 11{-}22. Hall P, Hosseini{-}Nasab M. 2006. On properties of functional principal components analysis. Journal of the Royal Statistical Society B 68: 109{-}126.

See Also

See Also as: fregre.pc, summary.fregre.fd and predict.fregre.fd. Alternative method: fregre.basis.cv and fregre.np.cv.

Examples

data(tecator)
absorp=tecator$absorp.fdata
ind=1:129
x=absorp[ind,]
y=tecator$y$Fat[ind]
out=fregre.pc.cv(x,y,7,"SICc")
out$pc.opt
summary(out$fregre.pc)