Information matrix for the Poisson process likelihood

The function returns the expected or observed information matrix.

Usage

pp.infomat(par, dat, method = c("obs", "exp"), u, np = 1, nobs = length(dat))

Arguments

par: vector of loc, scale and shape
dat: sample vector
method: string indicating whether to use the expected ('exp') or the observed ('obs' - the default) information matrix.
u: threshold
np: number of periods of observations. This is a post hoc adjustment for the intensity so that the parameters of the model coincide with those of a generalized extreme value distribution with block size length(dat)/np.
nobs: number of observations for the expected information matrix. Default to length(dat) if dat is provided.

Value

information matrix of the NHPP

Note

For the expected information matrix, the number of points above the threshold is random, but should correspond to np\(\Lambda\). The parametrization for np is shared between fit.pp, pp.ll, etc. The entries for the information matrix are given in Sharkey and Tawn (2017), but contains some typos which were corrected.

References

Sharkey, P. and J.A. Tawn (2017). A Poisson process reparameterisation for Bayesian inference for extremes, Extremes, 20(2), 239-263, http://dx.doi.org/10.1007/s10687-016-0280-2.

Examples

if (FALSE) {
dat <- rgp(n <- 1e3, 0.1, 2, -0.1)
np <- 10
mle <- fit.pp(dat, threshold = 0, np =  np)$par
info_obs <- pp.infomat(par = mle, dat = dat, method = "obs", u = 0, np = np)
info_exp <- pp.infomat(par = mle, dat = dat, method = "exp", u = 0, np = np)
info_obs/info_exp
}