svd hidim regression

svdreg.R

# Try-out of Hastie, Tibshirani, & Friedman (ESL, 2009) p.659

# Generate high-dimensional dataset
beta <- -100:100/100
X <- matrix(rnorm(100*201), 100)
y <- X%*%beta + rnorm(100, 0, sqrt(crossprod(beta)))

# Ridge estimates
bhat_ridge <- solve(crossprod(X) + diag(rep(.1, 201)), crossprod(X, y))

# SVD estimates
s <- svd(X)
R <- s$u%*%diag(s$d)
V <- s$v
bhat_svd <- V%*%solve(crossprod(R), crossprod(R, y))

bhat_ridge ≈ bhat_svd

magic.