fda.usc (version 1.1.0)

dev.S: The deviance score .

Description

Returns the deviance of a fitted model object by GCV score.

Usage

dev.S(y, S, obs,family = gaussian(),off,offdf,criteria="GCV",
W = diag(1, ncol = ncol(S), nrow = nrow(S)), trim = 0, draw = FALSE,...)

Arguments

y

Matrix of set cases with dimension (n x m), where n is the number of curves and m are the points observed in each curve.

obs

observed response.

S

Smoothing matrix.

family

a description of the error distribution and link function to be used in the model. This can be a character string naming a family function, a family function or the result of a call to a family function. (See family

off

off

offdf

off, degrees of freedom

criteria

The penalizing function. By default "Rice" criteria. Possible values are "GCV", "AIC", "FPE", "Shibata", "Rice".

W

Matrix of weights.

trim

The alpha of the trimming.

draw

=TRUE, draw the curves, the sample median and trimmed mean.

...

Further arguments passed to or from other methods.

Value

• res
  Returns GCV score calculated for input parameters.

Details

up to a constant, minus twice the maximized log-likelihood. Where sensible, the constant is chosen so that a saturated model has deviance zero. $$GCV(h)=p(h) \Xi(n^{-1}h^{-1})$$ Where $$p(h)=\frac{1}{n} \sum_{i=1}^{n}{\Big(y_i-r_{i}(x_i)\Big)^{2}w(x_i)}$$ and penalty function $$\Xi()$$ can be selected from the following criteria: Generalized Cross-validation (GCV): $$\Xi_{GCV}(n^{-1}h^{-1})=(1-n^{-1}S_{ii})^{-2}$$ Akaike's Information Criterion (AIC): $$\Xi_{AIC}(n^{-1}h^{-1})=exp(2n^{-1}S_{ii})$$ Finite Prediction Error (FPE) $$\Xi_{FPE}(n^{-1}h^{-1})=\frac{(1+n^{-1}S_{ii})}{(1-n^{-1}S_{ii})}$$ Shibata's model selector (Shibata): $$\Xi_{Shibata}(n^{-1}h^{-1})=(1+2n^{-1}S_{ii})$$ Rice's bandwidth selector (Rice): $$\Xi_{Rice}(n^{-1}h^{-1})=(1-2n^{-1}S_{ii})^{-1}$$

References

Wasserman, L. All of Nonparametric Statistics. Springer Texts in Statistics, 2006. Hardle, W. Applied Nonparametric Regression. Cambridge University Press, 1994. Febrero-Bande, M., Oviedo de la Fuente, M. (2012). Statistical Computing in Functional Data Analysis: The R Package fda.usc. Journal of Statistical Software, 51(4), 1-28. http://www.jstatsoft.org/v51/i04/

See Also

See Also as GCV.S. Alternative method: CV.S

Examples

data(phoneme)
mlearn<-phoneme$learn
np<-ncol(mlearn)
tt<-mlearn[["argvals"]]
S1 <- S.NW(tt,2.5)
gcv1 <- dev.S(mlearn$data[1,],obs=(sample(150)), S1,off=rep(1,150),offdf=3)
gcv2 <- dev.S(mlearn$data[1,],obs=sort(sample(150)), S1,off=rep(1,150),offdf=3)