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Compute the critical value for the Poisson KBQD tests for Uniformity

Source: R/critical_value.R
poisson_CV.Rd

This function computes the empirical critical value for the U-statistics for testing uniformity on the sphere based on the centered poisson kernel.

Usage

poisson_CV(d, size, rho, B, Quantile)

Arguments

d

the dimension of generated samples.

size

the number of observations to be generated.

rho

the concentration parameter for the Poisson kernel.

B

the number of replications.

Quantile

the quantile of the distribution use to select the critical value.

Value

the critical value for the specified dimension, size and level.

Details

For each replication, a sample of d-dimensional observations from the uniform distribution on the Sphere are generated and the Poisson kernel-based U-statistic is computed. After B iterations, the critical value is selected as the Quantile of the empirical distribution of the computed test statistics.

References

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