Estimation of the bivariate lambda function of Wadsworth and Tawn (2013)

Usage

lambdadep(dat, qu = 0.95, method = c("hill", "mle", "bayes"), plot = TRUE)

Arguments

dat

an \(n\) by \(2\) matrix of multivariate observations

qu

quantile level on uniform scale at which to threshold data. Default to 0.95

method

string indicating the estimation method

plot

logical indicating whether to return the graph of lambda

The confidence intervals are based on normal quantiles. The standard errors for the hill are based on the asymptotic covariance and that of the mle derived using the delta-method. Bayesian posterior predictive interval estimates are obtained using ratio-of-uniform sampling with flat priors: the shape parameters are constrained to lie within the triangle, as are frequentist point estimates which are adjusted post-inference.

Value

a plot of the lambda function if plot=TRUE, plus an invisible list with components

w the sequence of angles in (0,1) at which the lambda values are evaluated
lambda point estimates of lambda
lower.confint 95
upper.confint 95

Examples

set.seed(12)
dat <- mev::rmev(n = 1000, d = 2, model = "log", param = 0.1)
lambdadep(dat, method = 'hill')

if (FALSE) {
lambdadep(dat, method = 'bayes')
lambdadep(dat, method = 'mle')
# With independent observations
dat <- matrix(runif(n = 2000), ncol = 2)
lambdadep(dat, method = 'hill')
}