pvaldens: Density Estimation of Data in the Unit Interval In bootruin: A Bootstrap Test for the Probability of Ruin in the Classical Risk Process

Description

This function computes density estimators for densities with the unit interval as support. One example of data with such a density are p-values. Currently, two methods are implemented that differ in the kernel function used for estimation.

Usage

 1 pvaldens(x, bw, rho, method = c("jh", "chen"))

Arguments

 x a numeric vector of data points between 0 and 1. bw a number indicating the bandwidth used for the density estimation. rho a number determining the correlation coefficient, only used if method = "jh" method a character string determining the kernel function that is used, see Details.

Details

Depending on which method is selected, a different kernel function is used for the estimation. Since the support of the estimated function is bounded, those kernel functions are location-dependent.

If method = "jh", a Gaussian copula-based kernel function according to Jones and Henderson (2007) is used. In this case the bandwidth can either be specified directly or as correlation coefficient: if rho > 0 denotes the correlation coefficient and h > 0 the bandwidth, then h^2 = 1 - rho. Note that rho and bw are mutually exclusive.

For method = "chen", the kernel function is based on a beta density, according to Chen (1999).

See the cited articles for more details.

Value

A function with a single vector-valued argument that returns the estimated density at any given point(s).

References

Jones, M. C. and Henderson, D. A. (2007) Kernel-Type Density Estimation on the Unit Interval. Biometrika, 94(4), pp. 977–984.

Chen, S. X. (1999) A Beta Kernel Estimation for Density Functions. Computational Statistics and Data Analysis, 31(2), pp. 131–145.