pk.test {QuadratiK}

Poisson kernel-based quadratic distance test of Uniformity on the sphere

Description

This function performs the kernel-based quadratic distance goodness-of-fit tests for Uniformity for spherical data using the Poisson kernel with concentration parameter rho.

Usage

pk.test(x, rho = NULL, B = 300, Quantile = 0.95)

## S4 method for signature 'ANY'
pk.test(x, rho = NULL, B = 300, Quantile = 0.95)

## S4 method for signature 'pk.test'
show(object)

Arguments

x

A numeric d-dim matrix of data points on the Sphere S^(d-1).

rho

Concentration parameter of the Poisson kernel function.

B

Number of iterations for critical value estimation of Un (default: 300).

Quantile

The quantile to use for critical value estimation, 0.95 is the default value.

object

Object of class pk.test

Value

An S4 object of class pk.test containing the results of the Poisson kernel-based tests. The object contains the following slots:

• method: String indicating that the Poisson Kernel-based test is performed.

• x Data matrix.

• Un The value of the U-statistic.

• CV_Un The empirical critical value for Un.

• H0_Vn A logical value indicating whether or not the null hypothesis is rejected according to Un.

• Vn The value of the V-statistic.

• CV_Vn The critical value for Vn computed following the asymptotic distribution.

• H0_Vn A logical value indicating whether or not the null hypothesis is rejected according to Vn.

• rho The value of concentration parameter used for the Poisson kernel function.

• B Number of replications for the critical value of the U-statistic.

References

Ding, Y., Markatou, M., Saraceno, G. (2023). “Poisson Kernel-Based Tests for Uniformity on the d-Dimensional Sphere.” Statistica Sinica. doi: doi:10.5705/ss.202022.0347

Examples

# create a pk.test object
x_sp <- sample_hypersphere(3, n_points=100)
unif_test <- pk.test(x_sp,rho=0.8)
unif_test