TwoStage: Two-Stage Extreme Conditional Quantile Estimator

In EXRQ: Extreme Regression of Quantiles

Description

This function provides the Two-Stage estimator in Wang, Li and He (2012) for conditional extreme quantiles based on covariate-dependent extreme value index estimation. The intermediate conditional quantile is estimated by quantile regression of the response on the original scale without any transformation. The method is based on Hill estimator for the extreme value index and works for heavy-tailed distributions.

Usage

TwoStage(y, x, xstar, tau.e, k, tol = 1e-04)

Arguments

y	a vector of length n representing the response
x	a n x p matrix of n observations and p predictors
xstar	a m x p matrix of m observations and p predictors representing the covariate of interest
tau.e	the extreme quantile level of interest
k	the number of upper order statistics used in Hill estimator
tol	the tolerance level used for checking quantile crossing

Value

A list of the following commponents is returned

Q2Stage: the estimated (extrapolated) conditional extreme quantile of the response given x=xstar at the quantile level tau.e

gamma.x: the estimated covariate-dependent extreme value index (Hill estimator associated with x=xstar)

References

Wang, H., Li, D., and He, X. (2012). Estimation of high conditional quantiles for heavytailed distributions, Journal of the American Statistical Association, 107, 1453-1464.

See Also

ThreeStage

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))
## 2Stage method in Wang, Li and He (2012), no transformation
out.2stage <- TwoStage(y, x, xstar, tau.e, k=50)

Example output

Loading required package: quantreg
Loading required package: SparseM

Attaching package: 'SparseM'

The following object is masked from 'package:base':

    backsolve

Loading required package: mnormt

EXRQ documentation built on May 1, 2019, 7:26 p.m.