MU_fourier: Auxiliary function that computes the singular values of the...
In RandomCoefficients: Adaptive Estimation in the Linear Random Coefficients Models

Description Usage Arguments Value Examples

Auxiliary function that computes the singular values of the SVD of the operator F_c in Gaillac and Gautier 2018 using the Fast Fourier transform for the integration.

1	MU_fourier(psi, xseq, splin)

`psi`	Prolate spheroidal wave functions
`xseq`	grid on which to evaluate them, output of the Legendre quadrature
`splin`	use interpolation by splines or not (boolean).

library(orthopolynom)
library(polynom)
library(tmvtnorm)
library(ks)
library(sfsmisc)
library(snowfall)
library(fourierin)
library(rdetools)
library(statmod)
library(RCEIM)
library(robustbase)
library(VGAM)
library(RandomCoefficients)
#### Bandwidth 1
L =15
L1 = L+1
N2 = max(L,3)
twoN = 2*N2
#### Bandwidth 1
c1 = 1
K1 = max(twoN+2,30)
K = K1
c = 1
b=1
bound=1
out <- get_psi_mu(c,N2,twoN,K, L1)
Psi <- out[[1]]
mu<- out[[2]]
xseq = seq(-bound,bound, length.out=10)
resol=2^7
psix <- PSI_mu_fourier(xseq,c,b,Psi,resol)
psi <- psix[[1]]
xseq <- psix[[2]]
xseq2 <- xseq/b
splin =FALSE
mu_ev<- MU_fourier(psi,xseq,splin)
mu <- mu_ev[[1]]