Test for truncated GPD tails
Test between non-truncated GPD tails (light truncation) and truncated GPD tails (rough truncation).
trTestMLE(data, gamma, tau, alpha = 0.05, plot = TRUE, main = "Test for truncation", ...)
data |
Vector of n observations. |
gamma |
Vector of n-1 estimates for the EVI obtained from |
tau |
Vector of n-1 estimates for the τ obtained from |
alpha |
The used significance level, default is |
plot |
Logical indicating if the P-values should be plotted as a function of k, default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
We want to test H_0: X has non-truncated GPD tails vs. H_1: X has truncated GPD tails. Let \hat{γ}_k and \hat{τ}_k be the truncated MLE estimates for γ and τ. The test statistic is then
T_{k,n}=k (1+\hat{τ} (X_{n,n}-X_{-k,n}) )^{-1/\hat{ξ}_k}
which is asymptotically standard exponentially distributed. We reject H_0 on level α if T_{k,n}>\ln (1/{α)}. The corresponding P-value is given by \exp(-T_{k,n}).
See Beirlant et al. (2017) for more details.
A list with following components:
k |
Vector of the values of the tail parameter k. |
testVal |
Corresponding test values. |
critVal |
Critical value used for the test, i.e. \ln(1/α). |
Pval |
Corresponding P-values. |
Reject |
Logical vector indicating if the null hypothesis is rejected for a certain value of |
Tom Reynkens.
Beirlant, J., Fraga Alves, M. I. and Reynkens, T. (2017). "Fitting Tails Affected by Truncation". Electronic Journal of Statistics, 11(1), 2026–2065.
# Sample from GPD truncated at 99% quantile gamma <- 0.5 sigma <- 1.5 X <- rtgpd(n=250, gamma=gamma, sigma=sigma, endpoint=qgpd(0.99, gamma=gamma, sigma=sigma)) # Truncated ML estimator trmle <- trMLE(X, plot=TRUE, ylim=c(0,2)) # Test for truncation trTestMLE(X, gamma=trmle$gamma, tau=trmle$tau)
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