Graph equivalent of the Von Neummann variance estimator.
Usage
GVN(y, A, L)
Arguments
y
Noisy data.
A
Adjacency matrix.
L
Laplacian matrix.
References
von Neumann, J. (1941). Distribution of the ratio of the mean square successive difference to the variance. Ann. Math. Statistics, 35(3), 433--451.
de Loynes, B., Navarro, F., Olivier, B. (2021). Data-driven thresholding in denoising with Spectral Graph Wavelet Transform. Journal of Computational and Applied Mathematics, Vol. 389.
data(minnesota)
A <- minnesota$A
L <- laplacian_mat(A)
x <- minnesota$xy[ ,1]
n <- length(x)
f <- sin(x)
sigma <- 0.1
noise <- rnorm(n, sd = sigma)
y <- f + noise
sigma^2GVN(y, A, L)