expressions for the mean squared error (MSE) of the BLUE estimator for multiple noise distributions with positive support are provided. Given hyperparameter $\theta$, the MVU estimator for each noise distribution $p_e$ is denoted by $\hat{x}_{\mathrm{MVU}}^{p_e}(y_{1:N},\theta)$. MVU estimators with unknown hyperparameter are denoted by $\hat{x}_{\mathrm{MVU}}^{p_e}(y_{1:N})$. If the MVU cannot be found, an unbiased order-statistics-based estimator is derived and denoted by $\hat{x}^{p_e}(y_{1:N},\theta)$ and $\hat{x}^{p_e}(y_{1:N})$ for known and unknown hyperparameter cases, respectively. For example, $\hat{x}^{\mathcal{U}}_{\mathrm{MVU}}(y_{1:N},\beta)$ denotes the MVU estimator when $e_k\sim\mathcal{U}[0,\beta]$ and $\beta$ is known. $\hat{x}^{\mathcal{U}}_{\mathrm{MVU}}(y_{1:N})$, on the other hand, corresponds to the MVU estimator of uniform noise with unknown hyper parameters of the distribution. Table \[tbl:notation\] summarizes the notation used throughout this work.

  --------------------------------------------------------- ------------------------------------------------------------
  $\{y_k\}_{k=1}^N$                                         noisy measurements of the unknown parameter $x$
  \[2mm\] $\left(y^{(m)}\right)_{m=1}^N$                    ordered measurement sequence
  \[2mm\] $\theta$                                          parameters of the noise distribution
  \[2mm\] $\delta(\theta)$                                  bias compensation term
  \[2mm\] $\hat{x}^{p_e}_{\mathrm{BLUE}}(y_{1:N},\theta)$   BLUE when $e_k\sim p_e$ for known $\theta$
  \[2mm\] $\hat{x}^{p_e}_{\mathrm{MVU}}(y_{1:N},\theta)$    MVU estimator when $e_k\sim p_e$ for known $\theta$
  \[2mm\] $\hat{x}^{p_e}_{\mathrm{MVU}}(y_{1:N})$           MVU estimator when $e_k\sim p_e$ for unknown $\theta$
  \[2mm\] $\hat{x}^{p_e}(y_{1:N},\theta)$                   unbiased estimator when $e_k\sim p_e$ for known $\theta$
  \[2mm\] $\hat{x}^{p_e}(y_{1:N})$                          unbiased estimator when $e_k\sim p_e$ for unknown $\theta$
  --------------------------------------------------------- ------------------------------------------------------------

  : Notation.

\[tbl:notation\]

For each noise distribution, we also consider the 