texmex (version 1.3)

texmex-package: Conditional multivariate extreme values modelling.

Description

Conditional multivariate extreme values modelling following the approach of Heffernan and Tawn, 2004.

Details

ll{ Package: mex Type: Package Version: 1.2 Date: 2011-10-06 License: GPL (>=2) | BSD } gpd: Fit generalized Pareto distributions to data, possibly with covariates. Use maximum likelihood estimation, maximum penalized likelihood estimation or simulate from the posterior distribution.

mex: Fit multiple, independent generalized Pareto models to the the upper tails of the columns of a data set, and estimate the conditional dependence structure between the columns using the method of Heffernan and Tawn.

bootmex: Bootstrap estimation for parameters in generalized Pareto models and in the dependence structure. declust: Estimation of extremal index and subsequent declustering of dependent sequences using the intervals estimator of Ferro and Segers.

validate.texmex: Use the RUnit package to run lots of tests to establish a high degree of confidence that the functions do what they are supposed to.

References

J. E. Heffernan and J. A. Tawn, A conditional approach for multivariate extreme values, Journal of the Royal Statistical society B, 66, 497 -- 546, 2004. C.A.T Ferro and J. Segers, Inference for Clusters of Extreme Values, Journal of the Royal Statistical society B, 65, 545 -- 556, 2003.

Examples

# Analyse the winter data used by Heffernan and Tawn
mymex <- mex(winter, mqu = .7, penalty="none", dqu=.7, which = "NO")
plot(mymex)
# Only do 20 replicates to keep CRAN happy. Do many more in any
# real application
myboot <- bootmex(mymex, R=20)
plot(myboot)
mypred <- predict(myboot,  pqu=.95)
summary(mypred , probs = c( .025, .5, .975 ))

# Analyse the liver data included in the package
library(MASS) # For the rlm function

liver <- liver[liver$ALP.M > 1,] # Get rid of outlier
liver$ndose <- as.numeric(liver$dose)

alt <- resid(rlm(log(ALT.M) ~ log(ALT.B) + ndose, data=liver, method="MM"))
ast <- resid(rlm(log(AST.M) ~ log(AST.B) + ndose, data=liver, method="MM"))
alp <- resid(rlm(log(ALP.M) ~ log(ALP.B) + ndose, data=liver, method="MM"))
tbl <- resid(rlm(log(TBL.M) ~ log(TBL.B) + ndose, data=liver, method="MM"))

r <- data.frame(alt=alt, ast=ast, alp=alp, tbl=tbl)

Amex <- mex(r[liver$dose == "A",], mqu=.7)
Bmex <- mex(r[liver$dose == "B",], mqu=.7)
Cmex <- mex(r[liver$dose == "C",], mqu=.7)
Dmex <- mex(r[liver$dose == "D",], mqu=.7)

par(mfcol=c(3,3))
plot(Amex)

plot(Dmex, col="blue")

## Take a closer look at the marginal behaviour of ALT

r$ndose <- liver$ndose

altmod1 <- gpd(alt, qu=.7, phi = ~ ndose, xi = ~ ndose, data=r)
altmod2 <- gpd(alt, qu=.7, phi = ~ ndose, data=r)
altmod3 <- gpd(alt, qu=.7, xi = ~ ndose, data=r)
altmod4 <- gpd(alt, qu=.7, data=r)

# Prefer model 3, with term for xi on basis of AIC

# Lines commented out to keep CRAN happy
#balt3 <- gpd(alt, qu=.7, xi = ~ ndose, data=r, method="simulate")
#par(mfrow=c(3,3))
#plot(balt3)

# use longer burn-in and also thin the output

#balt3 <- thinAndBurn(balt3,burn=1000,thin=5)
#plot(balt3)

# Get some simulated values for dose D

#DParam <- predict(balt3,type="lp",newdata=data.frame(ndose=4),all=TRUE)[[1]]

#simD <- rgpd(nrow(DParam), sigma=exp(DParam[,"phi"]), xi=DParam[,"xi"], u=quantile(alt, .7))

# These are simulated residuals. Get some baselines and transform all
# to raw scale

#b <- sample(log(liver$ALT.M), size=nrow(balt3$param), replace=TRUE)
#res <- exp(b + simD)

# estimate quantiles on raw scale
#quantile(res, prob=c(.5, .75, .9, .95, .99))

# estimate proportion exceeding 3*upper limit of normal
#mean(res > 36 * 3) # 36 is the upper limit of normal for ALT