rlarg.fit: Maximum-likelihood Fitting of Order Statistics Model

Description

Maximum-likelihood fitting for the order statistic model, including generalized linear modelling of each parameter.

Usage

rlarg.fit(xdat, r = dim(xdat)[2], 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, …)

Arguments

xdat

A numeric matrix of data to be fitted. Each row should be a vector of decreasing order, containing the largest order statistics for each year (or time period). The first column therefore contains annual (or period) maxima. Only the first r columns are used for the fitted model. By default, all columns are used. If one year (or time period) contains fewer order statistics than another, missing values can be appended to the end of the corresponding row.

The largest r order statistics are used for the fitted model.

ydat

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 number of rows of xdat.

mul, sigl, shl

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).

mulink, siglink, shlink

Inverse link functions for generalized linear modelling of the location, scale and shape parameters repectively.

muinit, siginit, shinit

numeric of length equal to total number of parameters used to model the location, scale or shape parameter(s), resp. See Details section for default (NULL) initial values.

show

Logical; if TRUE (the default), print details of the fit.

method

The optimization method (see optim for details).

maxit

The maximum number of iterations.

…

Other control parameters for the optimization. These are passed to components of the control argument of optim.

Value

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 nllh, mle and se are always printed.

trans

An logical indicator for a non-stationary fit.

model

A list with components mul, sigl and shl.

link

A character vector giving inverse link functions.

conv

The convergence code, taken from the list returned by optim. A zero indicates successful convergence.

nllh

The negative logarithm of the likelihood evaluated at the maximum likelihood estimates.

data

The data that has been fitted. For non-stationary models, the data is standardized.

mle

A vector containing the maximum likelihood estimates.

cov

The covariance matrix.

A vector containing the standard errors.

vals

A matrix with three columns containing the maximum likelihood estimates of the location, scale and shape parameters at each data point.

The number of order statistics used.

Details

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).

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.

Examples

Run this code

# NOT RUN {
data(venice)
# }
# NOT RUN {
rlarg.fit(venice[,-1])
# }