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

## Description

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.

## Usage

 `1` ```MU_fourier(psi, xseq, splin) ```

## Arguments

 `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).

mu

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37``` ```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[] mu<- out[] xseq = seq(-bound,bound, length.out=10) resol=2^7 psix <- PSI_mu_fourier(xseq,c,b,Psi,resol) psi <- psix[] xseq <- psix[] xseq2 <- xseq/b splin =FALSE mu_ev<- MU_fourier(psi,xseq,splin) mu <- mu_ev[] ```

RandomCoefficients documentation built on June 7, 2019, 5:02 p.m.