Expected prediction error of the OLS fit

Formula: EPE(x_o) = sigma2 (1 + sum_j (x*_oj)^2 / lambda_j) with x* = Gamma'x_o and lambda_j the eigenvalues of X'X (p.80): nearly dependent features drive some lambda_j toward zero and blow the prediction error up.

Usage

Msm334(sigma2, x_star, eigenvalues)

Arguments

sigma2: Irreducible error variance.
x_star: Rotated feature vector Gamma'x_o.
eigenvalues: Eigenvalues of X'X, all strictly positive.

Value

List with estimate, irreducible, variance_inflation, method.

References

Montesinos Lopez, Montesinos Lopez & Crossa (2022), Multivariate Statistical Machine Learning Methods for Genomic Prediction, Springer, sec. 3.5 p.80. DOI 10.1007/978-3-030-89010-0.

Examples

if (morie_crypto_liboqs_available()) {
  Msm334(sigma2 = c(1, 2, 3, 4, 5, 6, 7, 8), x_star = c(1, 2, 3, 4, 5, 6, 7, 8),
    eigenvalues = c(1, 2, 3, 4, 5, 6, 7, 8))
}