[R] loess: choose span to minimize AIC?

[Michael Friendly]

Is there an R implementation of a scheme for automatic smoothing
parameter selection with loess, e.g., by minimizing one of the AIC/GCV 
statistics discussed by Hurvich, Simonoff & Tsai (1998)?

Below is a function that calculates the relevant values of AICC,
AICC1 and GCV--- I think, because I to guess from the names of the
components returned in a loess object.

I guess I could use optimize(), or do a simple line search on span=,
but I'm not sure how to use loess.aic to write a function
that would act as a wrapper for loess() and return the mimimizing
loess fit for a specified criterion.

loess.aic <- function (x) {
	# extract values from loess object
	if (!(inherits(x,"loess"))) stop("Error: argument must be a loess object")
	span <- x$pars$span
	n <- x$n
	traceL <- x$trace.hat
	sigma2 <- sum( x$residuals^2 ) / (n-1)
	delta1 <- x$one.delta
	delta2 <- x$two.delta
	enp <- x$enp

	aicc <- log(sigma2) + 1 + 2* (2*(traceL+1)) / (n-traceL-2)
	aicc1<- n*log(sigma2) + n* ( 
(delta1/(delta2*(n+enp)))/(delta1^2/delta2)-2 )
	gcv  <- n*sigma2 / (n-traceL)^2
	
	result <- list(span=span, aicc=aicc, aicc1=aicc1, gcv=gcv)
	return(result)
}


 > cars.lo <- loess(dist ~ speed, cars)
 >
 > (values <- loess.aic(cars.lo))
$span
[1] 0.75

$aicc
[1] 6.93678

$aicc1
[1] 167.7267

$gcv
[1] 5.275487

 >


-- 
Michael Friendly     Email: friendly AT yorku DOT ca
Professor, Psychology Dept.
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