Bias correction for GEV distribution

Bias corrected estimates for the generalized extreme value distribution using Firth's modified score function or implicit bias subtraction.

Usage

gev.bcor(par, dat, corr = c("subtract", "firth"), method = c("obs", "exp"))

Arguments

par: parameter vector (scale, shape)
dat: sample of observations
corr: string indicating which correction to employ either subtract or firth
method: string indicating whether to use the expected ('exp') or the observed ('obs' --- the default) information matrix. Used only if corr='firth'

Value

vector of bias-corrected parameters

Details

Method subtractsolves $$\tilde{\boldsymbol{\theta}} = \hat{\boldsymbol{\theta}} + b(\tilde{\boldsymbol{\theta}}$$ for $\tilde{\boldsymbol{\theta}}$, using the first order term in the bias expansion as given by gev.bias.

The alternative is to use Firth's modified score and find the root of $$U(\tilde{\boldsymbol{\theta}})-i(\tilde{\boldsymbol{\theta}})b(\tilde{\boldsymbol{\theta}}),$$ where $U$ is the score vector, $b$ is the first order bias and $i$ is either the observed or Fisher information.

The routine uses the MLE (bias-corrected) as starting values and proceeds to find the solution using a root finding algorithm. Since the bias-correction is not valid for $\xi < -1/3$, any solution that is unbounded will return a vector of NA as the solution does not exist then.

Examples

set.seed(1)
dat <- mev::rgev(n=40, loc = 1, scale=1, shape=-0.2)
par <- mev::fit.gev(dat)$estimate
gev.bcor(par, dat, 'subtract')
#>        loc      scale      shape 
#>  1.0069581  0.9460791 -0.2291570 
gev.bcor(par, dat, 'firth') #observed information
#>        loc      scale      shape 
#>  1.0042124  0.9378109 -0.2387444 
gev.bcor(par, dat, 'firth','exp')
#>        loc      scale      shape 
#>  0.9933414  0.9475920 -0.1991981