mrfDepth (version 1.0.12)

symtest: Test for angular symmetry around a specified center for bivariate data

Description

A test based on halfspace depth for angular symmetry of the bivariate data set x around the point z. The test is only valid when x contains no duplicates.

Usage

symtest(x, z, options=list())

Arguments

x

An \(n\) by 2 data matrix.

z

A vector of length \(2\).

options

A list of options to pass to hdepth. See hdepth for more information.

Value

pval

The \(p\)-value of the hypothesis test.

Details

The following hypothesis test is performed: H0: The data come from a continuous distribution \(P\) which is angularly symmetric about z. The test statistic being used is the halfspace depth of z with respect to x. Under the null hypothesis the halfspace depth of z equals \(1/2\). The distribution of the teststatistic under H0 is \(F_n(k) = P(hdepth(P, z) \le k)\). The \(p\)-value of the test is \(F_n(k)\) with \(k= hdepth(x,z)\).

References

Rousseeuw, P.J, Struyf, A. (2002). A Depth Test for Symmetry, in: Goodness-of-Fit Tests and Model Validity, Birkh<U+00E4>user Boston, pp.401--412.

Examples

# NOT RUN {
# Perform the test on a simple data example.
data(cardata90)
symtest(x = cardata90, z = hdepthmedian(cardata90)$median)
plot(cardata90)
# }