schedastic.test: Test on the effect of concomitant covariate on the extremes...

In ExtremeRisks: Extreme Risk Measures

Test on the effect of concomitant covariate on the extremes of the response variable

Description

Given observed data, perform a Kolmogorov-Smirnov type test comparing the cumulative distribution function of the concomitant covariate, defined as X \mid Y > t, with t being the threshold, against the cumulative distribution function of the random vector of covariate.

Usage

schedastic.test(data, k, M = 1000L, xg, ng, bayes = TRUE, C = 5L, alpha = 0.05)

Arguments

data	design matrix of dimension n by 2 containing the complete data for the dependent variable (first column) and covariate (second column) in [0,1]
k	integer, number of exceedances for the generalized Pareto
M	integer, number of samples to draw from the posterior distrinution of the law of the concomitant covariate. Default: 1000
xg	vector of covariate grid of dimension ng by 1 containing a sequence between zero and the last value of the corresponding covariate
ng	length of covariate grid
bayes	logical indicating the bootstrap method. If FALSE, a frequentist bootstrap on the empirical cumulative distribution function of the concomitant covariate is performed. Default to TRUE
C	integer, hypermparameter entering the posterior distributyion of the law of the concomitant covariate. Default: 5
alpha	double, significance level for the critical value of the test, computed as the (1-alpha) level empirical quantile of the sample of distances between the empirical cumulative distribution function of the concomitant and complete covariate. Default: 0.05

Value

a list with components

• Delta maximum observed distance between the empirical distribution functions of the concomitant and complete covariate

• DeltaM vector of length M containing the sample of maximum distances between the empirical distribution function of the concomitant complete covariate

• critical double, critical value for the test statistic, computed as the (1-alpha) level empirical quantile of DeltaM

• pval double, p-value

ExtremeRisks documentation built on Nov. 5, 2025, 7:05 p.m.