coeffs {USP} | R Documentation |
Calculate coefficients of a function's series expansion
Description
This function is used in InfKern to produce the kernel matrix from functional
data defined on the interval . For further details see Section 7.4
of (Berrett et al. 2021).
Usage
coeffs(X, Ntrunc)
Arguments
X |
The discretised functions whose coefficients are required.
This should be a matrix with one row per function, and with |
Ntrunc |
The number of coefficients that are required.
The function returns coefficients 1,..., |
Value
The coefficients of in its expansion in terms of sine functions.
See (Berrett et al. 2021) for more detail.
References
Berrett TB, Kontoyiannis I, Samworth RJ (2021). “Optimal rates for independence testing via U-statistic permutation tests.” Annals of Statistics, to appear.
Examples
t=seq(from=0,to=1,length.out=1000); X=t^2
U=coeffs(X,100)[1,]; L=5
plot(t,X,type="l")
approx=rep(0,1000)
for(l in 1:L){
approx=approx+qnorm(U[l])*sqrt(2)*sin((l-1/2)*pi*t)/((l-1/2)*pi)
lines(t,approx,col=l+1)
}
[Package USP version 0.1.2 Index]