| ThreeStage {EXRQ} | R Documentation |
Three-Stage Extreme Conditional Quantile Estimator
Description
Provides the estimation of extreme conditional quantile using the three-stage estimation method in Wang and Li (2013). Specifically the function estimates the tau.e-th conditional quantile of Y given x=xstar based on the power-transformed quantile regression model and extreme value theory. The method is based on Hill estimator for the extreme value index and works for heavy-tailed distributions (on the original scale).
Usage
ThreeStage(y, x, xstar, tau.e, grid.lam = seq(-2, 2, 0.1), grid.k, tau.lam,
a = 0, tol = 1e-04)
Arguments
y |
a vector of n responses |
x |
a n x p matrix of n observations and p predictors |
xstar |
a m x p matrix of m observations and p predictors |
tau.e |
the extreme quantile level of interest |
grid.lam |
the set of lambda (transformation parameter) values for grid search |
grid.k |
the grid for the number of upper order statistics involved in Hill estimator; used for searching for the data-adaptive k. If the lenfth of grid.k is 1, then k is fixed at grid.k and no selection is performed. |
tau.lam |
the quantile level used for estimating the transformation parameter |
a |
location shift parameter in the power transformation (introduced to avoid negative y values) |
tol |
the tolerance level for checking quantile crossing issue |
Value
A list is returned with the following components
lam: the estimated power-transformation parameter
k: the selected k, the number of upper order statistics involved in Hill estimator
gamma.x: the estimated x-dependent extreme value index (EVI)
cgmma: the pooled EVI estimation
Q3Stage: the three-stage estimator of the tau.e-th conditional quantile of Y given xstar based on the x-dependent EVI estimation
Q3StageP: the three-stage estimator of the tau.e-th conditional quantile of Y given xstar based on the pooled EVI estimation
References
Wang, H. and Li, D. (2013). Estimation of conditional high quantiles through power transformation. Journal of the American Statistical Association, 108, 1062-1074.
See Also
Examples
#A simulation example (sqrt transformation, heteroscedastic error)
library(EXRQ)
n=500
tau.e = c(0.99, 0.993, 0.995)
set.seed(12368819)
x1 = runif(n, -1, 1)
x2 = runif(n, -1, 1)
sqrty = 2 + x1 + x2 + (1+0.8*x1)*rpareto(n, 0.5)
x = as.matrix(cbind(x1, x2))
y = sqrty^2
xstar = rbind(c(-0.5,0),c(0,-0.5),c(0,0),c(0.5,0),c(0,0.5))
## 3Stage estimator
out.3stage <- ThreeStage(y, x, xstar, tau.e, grid.lam=seq(-0.5, 1.5, 0.1), grid.k=50, tau.lam=0.9)