dev.S

From fda.usc v2.0.1 by Manuel Oviedo de la Fuente

The deviance score

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

Keywords: utilities

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.

$$GCV(h)=p(h) \Xi(n^{-1}h^{-1})$$

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): $$\Xi_{Rice}(n^{-1}h^{-1})=(1-2n^{-1}S_{ii})^{-1}$$

Value

Returns GCV score calculated for input parameters.

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/

Examples

# NOT RUN {
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)

# }

Documentation reproduced from package fda.usc, version 2.0.1, License: GPL-2

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