ScaleReg: Scale estimator in regression

In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

Scale estimator in regression

Description

Estimator of the scale parameter in the regression case where \gamma is constant and the regression modelling is thus placed solely on the scale parameter.

Usage

ScaleReg(s, Z, kernel = c("normal", "uniform", "triangular", "epanechnikov", "biweight"), 
         h, plot = TRUE, add = FALSE, main = "Estimates of scale parameter", ...)

Arguments

s	Point to evaluate the scale estimator in.
Z	Vector of n observations (from the response variable).
kernel	The kernel used in the estimator. One of "normal" (default), "uniform", "triangular", "epanechnikov" and "biweight".
h	The bandwidth used in the kernel function.
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 "Estimates of scale parameter".
...	Additional arguments for the plot function, see plot for more details.

Details

The scale estimator is computed as

\hat{A}(s) = 1/(k+1) \sum_{i=1}^n 1_{Z_i>Z_{n-k,n}} K_h(s-i/n)

with K_h(x)=K(x/h)/h, K the kernel function and h the bandwidth. Here, it is assumed that we have equidistant covariates x_i=i/n.

See Section 4.4.1 in Albrecher et al. (2017) for more details.

Value

A list with following components:

k	Vector of the values of the tail parameter k.
A	Vector of the corresponding scale estimates.

Author(s)

Tom Reynkens

References

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

See Also

ProbReg, QuantReg, scale, Hill

Examples

data(norwegianfire)

Z <- norwegianfire$size[norwegianfire$year==76]

i <- 100
n <- length(Z)

# Scale estimator in i/n
A <- ScaleReg(i/n, Z, h=0.5, kernel = "epanechnikov")$A

# Small exceedance probability
q <- 10^6
ProbReg(Z, A, q, plot=TRUE)

# Large quantile
p <- 10^(-5)
QuantReg(Z, A, p, plot=TRUE)

ReIns documentation built on Nov. 3, 2023, 5:08 p.m.