influence_quan: Quantile for influence measures

In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

Quantile for influence measures

Description

Estimate the quantile of measures of influence for each observation.

Usage

influence_quan(model,out.influ,mue.boot=500,
smo=0.1,smoX=0.05,alpha=0.95,kmax.fix=FALSE,...)

Arguments

model	fregre.pc, fregre.basis or fregre.basis.cv object.
out.influ	inflluence.fd bject
mue.boot	Number of bootstrap samples
smo	Smoothing parameter as a proportion of response variance.
smoX	Smoothing parameter for fdata object as a proportion of variance-covariance matrix of the explanatory functional variable.
alpha	Significance level.
kmax.fix	The maximum number of principal comoponents or number of basis is fixed by model object.
...	Further arguments passed to or from other methods.

Details

Compute the quantile of measures of influence estimated in influence.fregre.fd for functional regression using principal components representation (fregre.pc) or basis representation
(fregre.basis or fregre.basis.cv).

A smoothed bootstrap method is used to estimate the quantiles of the influence measures, which allows to point out which observations have the larger influence on estimation and prediction.

Value

Return:

• quan.cook.for: Distance Cook Prediction Quantile.

• quan.cook.est: Distance Cook Estimation Quantile.

• quan.cook.Pena: Pena Distance Quantile.

• mues.est: Sample Cook generated.

• mues.pena: Sample Pena generated.

• beta.boot: Functional beta estimated by bootstrap method.

Author(s)

Manuel Febrero-Bande, Manuel Oviedo de la Fuente [e-mail]

References

Febrero-Bande, M., Galeano, P. and Gonzalez-Manteiga, W. (2010). Measures of influence for the functional linear model with scalar response. Journal of Multivariate Analysis 101, 327-339.

See Also

See Also as: influence.fregre.fd, fregre.basis, fregre.pc.

Examples

## Not run: 
data(tecator)
x=tecator$absorp.fdata
y=tecator$y$Fat
res=fregre.pc(x,y,1:6)

#time consuming
res.infl=influence.fregre.fd(res)
resquan=influence_quan(res,res.infl,4,0.01,0.05,0.95)
plot(res.infl$betas,type="l",col=2)
lines(res$beta.est,type="l",col=3)
lines(resquan$betas.boot,type="l",col="gray")

res=fregre.basis(x,y)
res.infl=influence.fregre.fd(res)
resquan=influence_quan(res,res.infl,mue.boot=4,kmax.fix=T)
plot(resquan$betas.boot,type="l",col=4)
lines(res.infl$betas,type="l",col=2)
lines(resquan$betas.boot,type="l",col="gray")

## End(Not run)

fda.usc documentation built on April 4, 2025, 4:35 a.m.