sumbasis {USP}

Kernel entries in infinite dimensional case

Description

Function to calculate each entry of the kernel matrix in the infinite dimensional example described in Section 7.4 of (Berrett et al. 2021). Here, a random function is converted to a sequence of coefficients and we use the Fourier basis on these coefficients. This function is only used in the function InfKern.

Usage

sumbasis(Ntrunc, M, x1, x2)

Arguments

Ntrunc

The total number of coefficients to look at.

M

The maximum frequency to look at in the Fourier basis.

x1

The coefficients of the first data point.

x2

The coefficients of the second data point.

Value

The entry of the kernel corresponding to the two data points.

References

Berrett TB, Kontoyiannis I, Samworth RJ (2021). “Optimal rates for independence testing via U-statistic permutation tests.” Annals of Statistics, to appear.

Examples

x1=runif(5); x2=runif(5); sumbasis(5,2,x1,x2)