Nonuniform Linear Regression With Block-Wise Sample-Minimum Preprocessing

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 nonuniform time samples. We show that this nonuniformity has negligible effect on the slope estimate variance, but introduces a spurious low-frequency component in the power spectrum, which can be detrimental for 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.