Maximum-likelihood fitting for the point process model, including generalized linear modelling of each parameter.
pp.fit(xdat, threshold, npy = 365, ydat = NULL, mul = NULL, sigl =
NULL, shl = NULL, mulink = identity, siglink = identity, shlink =
identity, muinit = NULL, siginit = NULL, shinit = NULL, show = TRUE,
method = "Nelder-Mead", maxit = 10000, …)A numeric vector of data to be fitted.
The threshold; a single number or a numeric
vector of the same length as xdat.
The number of observations per year/block.
A matrix of covariates for generalized linear modelling
of the parameters (or NULL (the default) for stationary
fitting). The number of rows should be the same as the length
of xdat.
Numeric vectors of integers, giving the columns
of ydat that contain covariates for generalized linear
modelling of the location, scale and shape parameters repectively
(or NULL (the default) if the corresponding parameter is
stationary).
Inverse link functions for generalized linear modelling of the location, scale and shape parameters repectively.
numeric giving initial parameter estimates. See Details section for information on default (NULL) initial values.
Logical; if TRUE (the default), print details of
the fit.
The optimization method (see optim for
details).
The maximum number of iterations.
Other control parameters for the optimization. These
are passed to components of the control argument of
optim.
A list containing the following components. A subset of these
components are printed after the fit. If show is
TRUE, then assuming that successful convergence is
indicated, the components nexc, nllh, mle
and se are always printed.
An logical indicator for a non-stationary fit.
A list with components mul, sigl
and shl.
A character vector giving inverse link functions.
The threshold, or vector of thresholds.
The number of observations per year/block.
The number of data points above the threshold.
The data that lie above the threshold. For non-stationary models, the data is standardized.
The convergence code, taken from the list returned by
optim. A zero indicates successful convergence.
The negative logarithm of the likelihood evaluated at the maximum likelihood estimates.
A matrix with four columns containing the maximum likelihood estimates of the location, scale and shape parameters, and the threshold, at each data point.
A matrix with three rows containing the maximum likelihood estimates of corresponding GPD location, scale and shape parameters at each data point.
A vector containing the maximum likelihood estimates.
The covariance matrix.
A vector containing the standard errors.
Different optimization methods may result in wildly different parameter estimates.
For non-stationary fitting it is recommended that the covariates
within the generalized linear models are (at least approximately)
centered and scaled (i.e.\ the columns of ydat should be
approximately centered and scaled). Otherwise, the numerics may
become unstable.
As of version 1.32, a more accurate estimate of the exceedance rate, in the face of covariates, is used (at the expense of computational efficiency). In particular, when including covariates, parameter estimates may differ from those in Coles (2001).
Let m=mean(xdat) and s=sqrt(6*var(xdat))/pi. Then, initial values assigend when 'muinit' is NULL are m - 0.57722 * s (stationary case). When 'siginit' is NULL, the initial value is taken to be s, and when 'shinit' is NULL, the initial value is taken to be 0.1. When covariates are introduced (non-stationary case), these same initial values are used by default for the constant term, and zeros for all other terms. For example, if a GEV( mu(t)=mu0+mu1*t, sigma, xi) is being fitted, then the initial value for mu0 is m - 0.57722 * s, and 0 for mu1.
Beirlant J, Goegebeur Y, Segers J and Teugels J. (2004). Statistics of Extremes, Wiley, Chichester, England.
Coles, Stuart (2001). An Introduction to Statistical Modeling of Extreme Values. Springer-Verlag, London.
# NOT RUN {
data(rain)
pp.fit(rain, 10)
# }
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