The stability test for symmetric alpha-stable distributions

Symmetric alpha-stable distributions are a popular statistical model for heavy-tailed phenomena encountered in communications, radar, biomedicine, and econometrics. The use of the symmetric alpha stable model is often supported by empirical evidence, where qualitative criteria are used to judge the fit, leading to subjective decisions. Objective decisions can only be made through quantitative statistical tests. Here, a goodness-of-fit hypothesis test for symmetric alpha-stable distributions is developed based on their unique stability property. Critical values for the test are found using both asymptotic theory and from bootstrap estimates. Experiments show that the stability test, using bootstrap estimates of the critical values, is better able to discriminate between symmetric alpha stable distributions and other heavy-tailed distributions than classical tests such as the Kolmogorov-Smirnov test.     

Detection of sources using bootstrap techniques

Source detection in array processing can be viewed as a test for equality of eigenvalues. Such a test is proposed, based on a multiple test procedure that considers all pairwise comparisons between eigenvalues. Using the bootstrap to estimate the null distributions of the test statistics results in a procedure with minimal assumptions on the nature of the signal. Simulations show that the proposed test is superior to information theoretic criteria such as the MDL, which are based on Gaussian signals and large sample sizes. Performance in most cases exceeds the more powerful sphericity test