dev.S: The deviance score

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

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.
S	Smoothing matrix.
obs	observed response.
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 for details of family functions.)
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.

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.

Where

and penalty function

can be selected from the following criteria:

Generalized Cross-validation (GCV):

Akaike's Information Criterion (AIC):

Finite Prediction Error (FPE)

Shibata's model selector (Shibata):

Rice's bandwidth selector (Rice):

Value

Returns GCV score calculated for input parameters.

Author(s)

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

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. https://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)

fda.usc documentation built on Oct. 17, 2022, 9:06 a.m.