estimating the mean $x$ observed in noise as $y_k=x+e_k$, for $k=1,2,\dots, N$, also known as “estimation of location" [@article:PI_kassam_85], where the noise $e_k$ has positive support. We will refer to such distributions as [*positive noise*]{}. Examples of distributions we will study include uniform, exponential, Rayleigh, Pareto.

A bias compensated linear estimator as the sample mean has a variance that decays as $1/N$, while it is well-known from the statistical literature, see for example [@book:ET_kay_93; @book:TPE_lehmann], that the minimum has a variance that decays as $1/N^2$. The minimum is the simplest example of order statistics. Certain care has to be taken for the cases where the parameters in the distributions are unknown, in which case bias compensation becomes tricky. This paper derives all combinations of known/unknown parameters for order statistics/BLUE (best linear unbiased estimator) for some selected and common distribution that allow for analytical solutions.

Problems involving positive noise can be motivated from applications where the arrival times of radio or sound waves are used. Such waves travel with the speed of the medium, and non line of sight conditions give rise to delayed arrival times. Physics does simply not allow for negative noise, only positive one. This case occur in 