R: Non-parametric Estimates for Dependence Functions of the...
amvnonpar
R Documentation
Non-parametric Estimates for Dependence Functions of the
Multivariate Extreme Value Distribution
Description
Calculate non-parametric estimates for the dependence function
A of the multivariate extreme value distribution and plot
the estimated function in the trivariate case.
A vector of length d or a matrix with d
columns, in which case the dependence function is evaluated
across the rows (ignored if plot is TRUE). The
elements/rows of the vector/matrix should be positive and should
sum to one, or else they should have a positive sum, in which
case the rows are rescaled and a warning is given.
A(1/d,…,1/d) is returned by default since it is often
a useful summary of dependence.
data
A matrix or data frame with d columns, which may
contain missing values.
d
The dimension; an integer greater than or equal to two.
The trivariate case d = 3 is the default.
epmar
If TRUE, an empirical transformation of the
marginals is performed in preference to marginal parametric
GEV estimation, and the nsloc argument is ignored.
nsloc
A data frame with the same number of rows as data,
or a list containing d elements of this type, for linear
modelling of the marginal location parameters. In the former case,
the argument is applied to all margins. The data frames are treated
as covariate matrices, excluding the intercept. Numeric vectors can
be given as alternatives to single column data frames. A list can
contain NULL elements for stationary modelling of selected
margins.
madj
Performs marginal adjustments. See
abvnonpar.
kmar
In the rare case that the marginal distributions are known,
specifies the GEV parameters to be used instead of maximum likelihood
estimates.
plot
Logical; if TRUE, and the dimension d is
three (the default dimension), the dependence function of a
trivariate extreme value distribution is plotted. For plotting in
the bivariate case, use abvnonpar. If FALSE
(the default), the following arguments are ignored.
col
A list of colours (see image). The first
colours in the list represent smaller values, and hence
stronger dependence. Each colour represents an equally spaced
interval between lower and one.
blty
The border line type, for the border that surrounds
the triangular image. By default blty is zero, so no
border is plotted. Plotting a border leads to (by default) an
increase in grid (and hence computation time), to ensure
that the image fits within it.
grid
For plotting, the function is evaluated at grid^2
points.
lower
The minimum value for which colours are plotted. By
default code{lower} = 1/3 as this is the theoretical
minimum of the dependence function of the trivariate extreme
value distribution.
ord
A vector of length three, which should be a permutation
of the set {1,2,3}. The points (1,0,0),
(0,1,0) and (0,0,1) (the vertices of the simplex)
are depicted clockwise from the top in the order defined by
ord. The argument alters the way in which the function
is plotted; it does not change the function definition.
lab
A character vector of length three, in which case the
ith margin is labelled using the ith component,
or NULL, in which case no labels are given. By default,
lab is as.character(1:3). The actual location of
the margins, and hence the labels, is defined by ord.
lcex
A numerical value giving the amount by which the
labels should be scaled relative to the default. Ignored
if lab is NULL.
Value
A numeric vector of estimates. If plotting, the smallest evaluated
estimate is returned invisibly.
Note
The rows of data that contain missing values are not used
in the estimation of the dependence structure, but every non-missing
value is used in estimating the margins.
The dependence function of the multivariate extreme value
distribution is defined in amvevd.
The function amvevd calculates and plots dependence
functions of multivariate logistic and multivariate asymmetric
logistic models.
The estimator plotted or calculated is a multivariate extension of
the bivariate Pickands estimator defined in abvnonpar.
See Also
amvevd, abvnonpar,
fgev
Examples
s5pts <- matrix(rexp(50), nrow = 10, ncol = 5)
s5pts <- s5pts/rowSums(s5pts)
sdat <- rmvevd(100, dep = 0.6, model = "log", d = 5)
amvnonpar(s5pts, sdat, d = 5)
## Not run: amvnonpar(data = sdat, plot = TRUE)
## Not run: amvnonpar(data = sdat, plot = TRUE, ord = c(2,3,1), lab = LETTERS[1:3])
## Not run: amvevd(dep = 0.6, model = "log", plot = TRUE)
## Not run: amvevd(dep = 0.6, model = "log", plot = TRUE, blty = 1)