ScaleReg function

Scale estimator in regression

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.

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

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.

Returns

A list with following components: - k: Vector of the values of the tail parameter $k$.

• A: Vector of the corresponding scale estimates.

References

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

Author(s)

Tom Reynkens

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)