EXRQ (version 1.0)

select.k.func: Selection of the Tuning Parameter k

Description

This function selects the tuning parameter k, the number of upper order statistics involved in Hill estimator of EVI among a grid of points following the method described in Section 3.3 of Wang and Li (2013). The method selects k as the value that minimizes the discrepancy between the estimated x-dependent EVI on the transformed scale and lam times the estimated x-dependent EVI on the original scale

Usage

select.k.func(y, x, Lam.y, lam, a, max.tau, grid.k, n)

Arguments

y

a vector of n untransformed responses

x

a n x p matrix of n observations and p predictors

Lam.y

a vector of n power-transformed responses

lam

the power-transformation parameter

a

location shift parameter in the power transformation (introduced to avoid negative y values)

max.tau

the upper bound of the intermediate quantile levels

grid.k

the grid for the number of upper order statistics involved in Hill estimator

n

the number of observations

Value

the selected k is returned

References

Wang, H. and Li, D. (2013). Estimation of conditional high quantiles through power transformation. Journal of the American Statistical Association, 108, 1062-1074.