Hill-type estimator for the conditional EVI
Hill-type estimator for the conditional Extreme Value Index (EVI) adapted for censored data.
crHill(x, Xtilde, Ytilde, censored, h,
kernel = c("biweight", "normal", "uniform", "triangular", "epanechnikov"),
logk = FALSE, plot = FALSE, add = FALSE, main = "", ...)x |
Value of the conditioning variable X to estimate the EVI at. |
Xtilde |
Vector of length n containing the censored sample of the conditioning variable X. |
Ytilde |
Vector of length n containing the censored sample of the variable Y. |
censored |
A logical vector of length n indicating if an observation is censored. |
h |
Bandwidth of the non-parametric estimator. |
kernel |
Kernel of the non-parametric estimator. One of |
logk |
Logical indicating if the Hill-type estimates are plotted as a function of \log(k) ( |
plot |
Logical indicating if the estimates should be plotted as a function of k, default is |
add |
Logical indicating if the estimates should be added to an existing plot, default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
This is a Hill-type estimator of the EVI of Y given X=x. The estimator uses the censored sample (\tilde{X}_i, \tilde{Y}_i), for i=1,…,n, where X and Y are censored at the same time. We assume that Y and the censoring variable are conditionally independent given X.
See Section 4.4.3 in Albrecher et al. (2017) for more details.
A list with following components:
k |
Vector of the values of the tail parameter k. |
gamma |
Vector of the corresponding Hill-type estimates. |
Tom Reynkens
Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.
# Set seed set.seed(29072016) # Pareto random sample Y <- rpareto(200, shape=2) # Censoring variable C <- rpareto(200, shape=1) # Observed (censored) sample of variable Y Ytilde <- pmin(Y, C) # Censoring indicator censored <- (Y>C) # Conditioning variable X <- seq(1, 10, length.out=length(Y)) # Observed (censored) sample of conditioning variable Xtilde <- X Xtilde[censored] <- X[censored] - runif(sum(censored), 0, 1) # Conditional Pareto QQ-plot crParetoQQ(x=1, Xtilde=Xtilde, Ytilde=Ytilde, censored=censored, h=2) # Plot Hill-type estimates crHill(x=1, Xtilde, Ytilde, censored, h=2, plot=TRUE)
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