bivquant (version 0.1)

bivquant: 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 \(\pi/2\) of length 10 is used.

tau

The quantile level. If not specified, the median, \(\tau=0.5\) 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.

Value

an object of class bivquant.

Details

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

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

# NOT RUN {
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")
# }