In a linear Gauss–Markov model, the parameter estimates from BLUUE (Best Linear Uniformly Unbiased Estimate) are not robust
against possible outliers in the observations. Moreover, by giving up the unbiasedness constraint, the mean squared error
(MSE) risk may be further reduced, in particular when the problem is ill-posed. In this paper, the α-weighted S-homBLE (Best homogeneously Linear Estimate) is derived via formulas originally used for variance component estimation on
the basis of the repro-BIQUUE (reproducing Best Invariant Quadratic Uniformly Unbiased Estimate) principle in a model with
stochastic prior information. In the present model, however, such prior information is not included, which allows the comparison
of the stochastic approach (α-weighted S-homBLE) with the well-established algebraic approach of Tykhonov–Phillips regularization, also known as R-HAPS (Hybrid APproximation Solution), whenever the inverse of the “substitute matrix” S exists and is chosen as the R matrix that defines the relative impact of the regularizing term on the final result.