An | R Documentation |
Bivariate and multivariate versions of the nonparametric rank-based
estimators of the Pickands dependence function A
, studied in
Genest and Segers (2009) and Gudendorf and Segers (2011).
An.biv(x, w, estimator = c("CFG", "Pickands"), corrected = TRUE,
ties.method = eval(formals(rank)$ties.method))
An(x, w, ties.method = eval(formals(rank)$ties.method))
x |
a data matrix that will be transformed to
pseudo-observations. If |
w |
if |
estimator |
specifies which nonparametric rank-based estimator
of the unknown Pickands dependence function to use in the bivariate
case; can be either
|
corrected |
TRUE means that the bivariate estimators will be corrected to ensure that their value at 0 and 1 is 1. |
ties.method |
|
More details can be found in the references.
An.biv()
returns a vector containing the values of the
estimated Pickands dependence function at the points in w
(and
is the same as former Anfun()
).
The function An
computes simultaneously the three corrected
multivariate estimators studied in Gudendorf and Segers (2011) at the
points in w
and retuns a list whose components are
P |
values of the Pickands estimator at the points in |
CFG |
values of the CFG estimator at the points in |
HT |
values of the Hall-Tajvidi estimator at the points in |
C. Genest and J. Segers (2009). Rank-based inference for bivariate extreme-value copulas. Annals of Statistics 37, 2990–3022.
G. Gudendorf and J. Segers (2011). Nonparametric estimation of multivariate extreme-value copulas. Journal of Statistical Planning and Inference 142, 3073–3085.
evCopula
, A
, and evTestA
.
Further, evTestC
, evTestK
,
exchEVTest
, and gofEVCopula
.
## True Pickands dependence functions
curve(A(gumbelCopula(4 ), x), 0, 1)
curve(A(gumbelCopula(2 ), x), add=TRUE, col=2)
curve(A(gumbelCopula(1.33), x), add=TRUE, col=3)
## CFG estimator
curve(An.biv(rCopula(1000, gumbelCopula(4 )), x), lty=2, add=TRUE)
curve(An.biv(rCopula(1000, gumbelCopula(2 )), x), lty=2, add=TRUE, col=2)
curve(An.biv(rCopula(1000, gumbelCopula(1.33)), x), lty=2, add=TRUE, col=3)
## Pickands estimator
curve(An.biv(rCopula(1000, gumbelCopula(4 )), x, estimator="Pickands"),
lty=3, add=TRUE)
curve(An.biv(rCopula(1000, gumbelCopula(2 )), x, estimator="Pickands"),
lty=3, add=TRUE, col=2)
curve(An.biv(rCopula(1000, gumbelCopula(1.33)), x, estimator="Pickands"),
lty=3, add=TRUE, col=3)
legend("bottomleft", paste0("Gumbel(", format(c(4, 2, 1.33)),")"),
lwd=1, col=1:3, bty="n")
legend("bottomright", c("true", "CFG est.", "Pickands est."), lty=1:3, bty="n")
## Relationship between An.biv and An
u <- c(runif(100),0,1) # include 0 and 1
x <- rCopula(1000, gumbelCopula(4))
r <- An(x, cbind(1-u, u))
all.equal(r$CFG, An.biv(x, u))
all.equal(r$P, An.biv(x, u, estimator="Pickands"))
## A trivariate example
x <- rCopula(1000, gumbelCopula(4, dim = 3))
u <- matrix(runif(300), 100, 3)
w <- u / apply(u, 1, sum)
r <- An(x, w)
## Endpoint corrections are applied
An(x, cbind(1, 0, 0))
An(x, cbind(0, 1, 0))
An(x, cbind(0, 0, 1))
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