Err(x0) = sigma^2 + bias^2 + |h(x0)|^2 sigma^2 with h(x0) = X (X'X)^-1 x0
(ESL eq 7.11); the in-sample average variance term is p sigma^2 / N (eq
7.12).
Usage
morie_esl_linear_prediction_error(X, x0, sigma2, bias2 = 0)
Arguments
- X
Design, N by p.
- x0
Point.
- sigma2
Noise variance.
- bias2
Squared bias at x0.
Value
Named list: variance, err_x0, in_sample_variance, h_norm2.
References
Hastie, Tibshirani & Friedman (2009), sec. 7.3.
Examples
morie_esl_linear_prediction_error(cbind(1, sin(1:20)), c(1, 0.3), 0.5)$err_x0
#> [1] 0.5280518
