A Simple Analysis of Linear Regression with Sample-Minimum Erlang Variates

We analyze the statistical properties of slope estimates obtained from linear linera 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 in 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 lineaa regression. These results are useful, for example, in precision clock synchronization over packet networks, where the random variates model packet arrival times.