Under \(Y = X\beta + \epsilon\), \(\epsilon \sim N_n(0, \sigma^2 I_n)\)
and a fixed design, returns the exact mean, second moment and mean squared
error of each coordinate of the STR estimator as an estimator of the
projection \(\theta = P_X \beta\), and the total risk
\(E\|\hat\theta - \theta\|_2^2\). No centring or scaling is applied:
X is used as supplied.
Usage
hr_risk(X, beta, sigma, k, gamma, nonneg = FALSE, scale = 1)
Arguments
- X
design matrix.
- beta
true coefficient vector.
- sigma
error standard deviation.
- k
ridge parameter.
- gamma
threshold.
- nonneg
logical, nonnegative variant.
- scale
For hr, logical training least-squares rescaling (SSTR-LS).
For hr_risk, a fixed positive numeric scale; not a random fitted scale.
Value
A list with components mean, second, mse,
risk, theta, m (mean of the ridge estimator) and
s (its coordinatewise standard deviations).
