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by Darryl N. Veitch, Patrice Abry
IEEE Transactions on Signal Processing
http://www.cubinlab.ee.mu.oz.au/~darryl/A4.ps.gz
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Abstract:
A wavelet based statistical test is described for distinguishing true time variation of the scaling exponent describing scaling behaviour, from statistical
uctuations of estimates across time of a constant exponent. The test is applicable to diverse scaling phenomena including long range dependence and exactly self-similar processes in a uniform framework, without the need for prior knowledge of the type in question. It is based on the special properties of wavelet-based estimates of the scaling exponent over adjacent blocks of data, strongly motivating an idealised inference problem: the equality or otherwise of means of independent Gaussian variables with known variances. A uniformly most powerful invariant test exists for this latter problem and is described. A separate UMPI test is also described for when the scaling exponent undergoes a level change. The power functions of the two tests are given explicitly and compared. Using simulation the eect in practice of deviations from the idealisations made of the statistical properties of the wavelet detail coecients are analysed and found to be small. The tests inherit the signicant robustness and computational advantages of the underlying wavelet-based estimator. A detailed methodology is given describing its use in practical situations. The use and benets of the test are illustrated on the Bellcore Ethernet data sets. Keywords: Self-similarity, long-range dependence, scaling exponent, wavelets, hypothesis testing, time constancy, stationarity, telecommunications networks. 1
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