SpatialExtremes (version 1.5-1)

TIC: Takeuchi's information criterion

Description

Computes a the Takeuchi's information criterion which is equivalent to the AIC when the model is miss-specified.

Usage

TIC(object, ..., k = 2)

Arguments

object

An object of class maxstab or spatgev. Often, it will be the output of the fitmaxstab or fitspatgev function.

...

Additional objects of class maxstab or spatgev for which TIC should be computed.

k

Numeric. The penalty per parameter to be used. The case k = 2 (default) correspond to the classical TIC and $k = \log n$, n number of observations, is the robust version of the BIC.

Value

• Numeric.

Details

TIC is like AIC so that when comparing models one wants to get the lowest TIC score.

References

Gao, X. and Song, P. X.-K. (2009) Composite likelihood Bayesian information criteria for model selection in high dimensional data. Preprint.

Sakamoto, Y., Ishiguro, M., and Kitagawa G. (1986) Akaike Information Criterion Statistics. D. Reidel Publishing Company.

Varin, C. and Vidoni, P. (2005) A note on composite likelihood inference and model selection. Biometrika 92(3):519--528.

See Also

fitmaxstab, AIC

Examples

##Define the coordinate of each location
n.site <- 50
locations <- matrix(runif(2*n.site, 0, 100), ncol = 2)
colnames(locations) <- c("lon", "lat")

##Simulate a max-stable process - with unit Frechet margins
data <- rmaxstab(40, locations, cov.mod = "whitmat", sill = 0.8, range =
30, smooth = 0.5)

M0 <- fitmaxstab(data, locations, "powexp", std.err.type = "score",
                 fit.marge = FALSE)
M1 <- fitmaxstab(data, locations, "cauchy", std.err.type = "score",
                 fit.marge = FALSE)

TIC(M0, M1)
TIC(M0, M1, k = log(nrow(data)))