ReIns: ScaleReg – R documentation

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ScaleReg

Scale estimator in regression

Description

Estimator of the scale parameter in the regression case where γ 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) ∑_{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.

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

Functions from "Reinsurance: Actuarial and Statistical Aspects"

v1.0.10

GPL (>= 2)

Authors

Tom Reynkens [aut, cre] (<https://orcid.org/0000-0002-5516-5107>), Roel Verbelen [aut] (R code for Mixed Erlang distribution, <https://orcid.org/0000-0002-2347-9240>), Anastasios Bardoutsos [ctb] (Original R code for cEPD estimator), Dries Cornilly [ctb] (Original R code for EVT estimators for truncated data), Yuri Goegebeur [ctb] (Original S-Plus code for basic EVT estimators), Klaus Herrmann [ctb] (Original R code for GPD estimator)

Initial release

2020-05-16