xasym {mev} | R Documentation |
Coefficient of extremal asymmetry
Description
This function implements estimators of the bivariate coefficient of extremal asymmetry proposed in Semadeni's (2021) PhD thesis. Two estimators are implemented: one based on empirical distributions, the second using empirical likelihood.
Usage
xasym(
data,
u = NULL,
nq = 40,
qlim = c(0.8, 0.99),
method = c("empirical", "emplik"),
confint = c("none", "wald", "bootstrap"),
level = 0.95,
B = 999L,
ties.method = "random",
plot = TRUE,
...
)
Arguments
data |
an |
u |
vector of probability levels at which to evaluate extremal asymmetry |
nq |
integer; number of quantiles at which to evaluate the coefficient if |
qlim |
a vector of length 2 with the probability limits for the quantiles |
method |
string indicating the estimation method, one of |
confint |
string for the method used to derive confidence intervals, either |
level |
probability level for confidence intervals, default to 0.95 or bounds for the interval |
B |
integer; number of bootstrap replicates (if applicable) |
ties.method |
string; method for handling ties. See the documentation of rank for available options. |
plot |
logical; if |
... |
additional parameters for plots |
Details
Let U
, V
be uniform random variables and define the partial extremal dependence coefficients
\varphi_{+}(u) = \Pr(V > U | U > u, V > u)
,
\varphi_{-}(u) = \Pr(V < U | U > u, V > u)
and
\varphi_0(u) = \Pr(V = U | U > u, V > u)
Define
\varphi(u) = \frac{\varphi_{+} - \varphi_{-}}{\varphi_{+} + \varphi_{-}}
The empirical likelihood estimator, derived for max-stable vectors with unit Frechet margins, is
\frac{\sum_i p_i I(w_i \leq 0.5) - 0.5}{0.5 - 2\sum_i p_i(0.5-w_i) I(w_i \leq 0.5)}
where p_i
is the empirical likelihood weight for observation i
and w_i
is the pseudo-angle associated to the first coordinate.
Value
an invisible data frame with columns
threshold
vector of thresholds on the probability scale
coef
extremal asymmetry coefficient estimates
confint
either
NULL
or a matrix with two columns containing the lower and upper bounds for each threshold
References
Semadeni, C. (2020). Inference on the Angular Distribution of Extremes, PhD thesis, EPFL, no. 8168.
Examples
## Not run:
samp <- rmev(n = 1000,
d = 2,
param = 0.2,
model = "log")
xasym(samp, confint = "wald")
xasym(samp, method = "emplik")
## End(Not run)