crosses are the numerical MSEs obtained from $M=5000$ repetitions. Both MVU estimators, with and without any knowledge of the hyper parameters of the underlying noise, result in noticeably less MSE compared to the BLUE estimator. The minimum order statistics estimator also outperforms BLUE when measurements are corrupted with additive, uniformly distributed, noise. It can be further observed that if the hyper parameter $\beta$ is unknown, the MSE of the proposed estimator is negligibly larger than the case with known $\beta$.

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For the exponential noise distribution, as shown in Figure \[fig:exponential\_blue\_mvu\_all\], there is still a non-negligible difference between BLUE and the other three estimators in terms of estimators’ MSE. However, the two MVU estimators, specially for large values of $N$, behave similarly. In order to verify their performance for smaller sample sizes, Figure \[fig:exponential\_blue\_mvu\_zoom\] illustrates the variances of all estimators for $N\leq 20$. At the beginning, $N\in[2,4]$ the estimator with unknown hyperparameter has the largest MSE. However, for larger sample sizes, the two MVU estimators are almost equal and both have less MSE than the BLUE estimator. As in case of uniformly distributed measurement noise, the minimum order statistics estimator outperforms BLUE specially for large sample sizes.

In case of 