This function estimates the noise level σ in linear regression with possible presence of outliers, based on "lasso-refitting" strategy.
the design matrix with the first column being 1 (the column of intercepts).
Assume the mean-shift model
y = X β + u + ε,
where ε ~ N(0, σ^2 I). This is equivalent to
y = X.enlarged β + ε,
where X.enlarged = (X : I_n). This function fits a lasso regression based on (y, X.enlarged) with the cross-validated tuning parameter, and then computes the residual sum of square, scaled by 1/(n-s), where s is the number of active variables estimated by lasso.
This function returns an estimate of the noise level σ.
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