crHill {ReIns}

Hill-type estimator for the conditional EVI

Description

Hill-type estimator for the conditional Extreme Value Index (EVI) adapted for censored data.

Usage

crHill(x, Xtilde, Ytilde, censored, h, 
       kernel = c("biweight", "normal", "uniform", "triangular", "epanechnikov"), 
       logk = FALSE, plot = FALSE, add = FALSE, main = "", ...)

Arguments

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 "biweight" (default), "normal", "uniform", "triangular" and "epanechnikov".

logk

Logical indicating if the Hill-type estimates are plotted as a function of \log(k) (logk=TRUE) or as a function of k. Default is FALSE.

plot

Logical indicating if the estimates should be plotted as a function of k, default is FALSE.

add

Logical indicating if the estimates should be added to an existing plot, default is FALSE.

main

Title for the plot, default is "" (no title).

...

Additional arguments for the plot function, see plot for more details.

Details

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,\ldots,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.

Value

A list with following components:

k

Vector of the values of the tail parameter k.

gamma

Vector of the corresponding Hill-type estimates.

Author(s)

Tom Reynkens

References

Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.

See Also

crParetoQQ, crSurv, cHill

Examples

# 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)