# testC.EVI: Testing the Constancy of EVI Over Covariates In EXRQ: Extreme Regression of Quantiles

## Description

This function tests whether the extreme value index of Y, gamma(x), is constant or varying across the covariate x by using the test procedure described in Section 3.4 of Wang and Li (2013).

## Usage

 ```1 2``` ```testC.EVI(y, x, grid.lam = seq(-2, 2, 0.1), grid.k, tau.lam = 0.9, u.x = 0, a = 0, M = 2, tol = 1e-04) ```

## Arguments

 `y` a vector of n untransformed responses `x` a n x p matrix of n observations and p predictors `grid.lam` a grid of points for power-transformation parameter `grid.k` a grid of points for k, the number of upper order statistics involved in Hill estimator `tau.lam` the quantile level used for estimating the transformation parameter `u.x` the proportion to be trimmed in the x direction `a` location shift parameter in the power transformation (introduced to avoid negative y values) `M` a constant larger than one that is used for estimating the c vector and thus K(x) function. The default is two `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 tuning parameter k, the number of upper order statistics involved in Hill estimator

Tm: the proposed test statistic

scaledTm: the standardized test statistic

pval.iid: the p-value based on iid assumption, that is, assuming that K(x)=1

pval.nid: the p-value based on estimated K(x)=(X'C)^(1/EVI)

gamma.bar: the pooled EVI estimator

hat.gamma: a N-dimensional vector consisting of the estimated x-dependent EVI at x=xstar

xstar: a N x p matrix of N observations and p predictors

## References

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```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 out = testC.EVI(y, x, grid.lam=seq(-0.5, 1.5, 0.1), grid.k=50, tau.lam=0.9) (Tval = out\$scaledTm) (pval.iid = out\$pval.iid) (pval.nid = out\$pval.nid) ```

EXRQ documentation built on May 29, 2017, 9:42 a.m.