Robust Estimation of the Self-similarity Parameter

Supplementary Webpage

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In Section 4.2 of the paper, we simulate fGn for H=0.5, 0.75 and 0.9. The SSB estimator and three robust regression estimators (IRLS, LTS and L1) are applied to estimate the Hurst parameter for 50 simulated traces. The estimates are compared in the following table.

  SSB IRLS LTS L1
H=0.5
bias -0.001 -0.000 -0.003 -0.002
SE 0.015 0.015 0.019 0.019
RMSE 0.015 0.015 0.019 0.019
H=0.75
bias 0.005 0.004 0.003 0.002
SE 0.015 0.015 0.018 0.018
RMSE 0.016 0.015 0.018 0.018
H=0.9
bias 0.006 0.004 0.001 0.002
SE 0.017 0.015 0.021 0.017
RMSE 0.018 0.016 0.021 0.018

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For the four traces analyzed in our paper, we plotted the original traces, the corresponding detrended traces and level shifts removed, along with both the standard and robust logscale diagrams.  PDF files are linked.

Trace Description Plot of the Trace Plot of the Detrended Trace Plot of the Level Shifts Removed Logscale Diagram
 
Abilene Oscillating level shifts Plot Plot Plot Plot
UNC02-APR-09 Few level shifts at the beginning Plot Plot Plot Plot
UNC02-APR-11 Missing values in the middle Plot Plot Plot Plot
Zoomed-in Plot Zoomed-in Plot Zoomed-in Plot
UNC02-APR-13 Many level shifts in the middle due to possible IP scan Plot Plot Plot Plot
Zoomed-in Plot Zoomed-in Plot Zoomed-in Plot

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Updated on October 15th, 2006.