A simple analysis of linear regression with sample-minimum Erlang variates

We analyze the statistical properties of slope estimates obtained from linear regression with sample-minimum Erlang variates. The sample-minimum of sequential blocks has the effect of introducing non-uniform time samples. It is shown that this non-uniformity has negligible effect on the slope estimate variance, but introduces a spurious low-frequency component in the power spectrum, which may be detrimental for ultra-low-bandwidth tracking applications. The analysis shows that this effect can be moderated by choosing a sufficiently large number of sample-minimum output samples in the linear regression. These results are useful, for example, in clock synchronization over packet networks, where the random variates model packet arrival times.