bivquant: Bivariate Quantiles

In bivquant: Estimation of Bivariate Quantiles

Description

This function fits the empirical bivariate quantiles based on the CDF (cumulative distrubtion function). We use linear programming. Currently, the solver is lp from the package lpSolve

Usage

bivquant(y, alphaseq = NULL, tau = NULL, transformed = FALSE)

Arguments

y	the responses in a matrix or data frame with 2 columns and rows equal to the number of observations.
alphaseq	The angles along which the quantile should be computed, can be a vector. If not specified, quantiles will will be computed for a equidistant grid from 0 to π/2 of length 10 is used.
tau	The quantile level. If not specified, the median, τ=0.5 will be computed.
transformed	Default is FALSE specifying that quantiles on the original scale are returned. If TRUE, quantiles on the unit square are returned in addition.

Details

The function imitates rotation around (1,1) in the transformed coordinate system and thus allows to estimate the marginal quantiles.

Value

an object of class bivquant.

Author(s)

Nadja Klein.

References

Nadja Klein and Thomas Kneib (2019). Directional Bivariate Quantiles - A Robust Approach based on the Cumulative Distribution Function. To appear in Advances in Statistical Analysis (AStA)

See Also

lp.

Examples

require("MASS")
require("mvtnorm")
set.seed(42)

tauseq <- seq(0.1,0.9,by=0.1) #quantile levels

alphas <- seq(0*pi/32,16*pi/32,by=0.5*pi/32) #grid of angles
n <- 50 #sample size

#generate bivariate data
mu <- c(6, 10)
#correlated responses
rho <- 0.5
Sigma <- matrix(c(
    1.0, rho,
    rho, 1.0
  ),
  ncol=2, byrow=TRUE)

X <- rmvnorm(n, mu, Sigma)
bivqu <- bivquant(X,alpha=alphas,tau=tauseq)
plot(bivqu, pch=20,col="grey")


#bigger n
set.seed(123)
n <- 100


X <- dgp_cop(n, family="clayton", margins=c("norm", "norm"),
		 paramMargins=list(list(mean = 4, sd = 1), list(mean = 4, sd = 5)),
		 rho=1.75)


bivqu <- bivquant(X,alpha=alphas,tau=tauseq)
plot(bivqu, pch=20,col="grey")

bivquant documentation built on Aug. 28, 2019, 5:05 p.m.