A Nonparametric Sequential Test with Power 1 for the Mean of Lévy-stable Laws with Infinite Variance
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A nonparametric sequential test with power one for the mean of Lévy-stable laws with infinite variance is given. Our considerations are based on a law of the iterated logarithm for Peng’s estimator [Peng, Stat. Probab. Lett., 52:255–264, 2001] of the mean of heavy-tailed distributions. Our main motivation comes from applications to financial data, and in particular to sequential control of daily asset returns.
KeywordsHeavy tails Hill’s estimator Lévy-stable law Law of the iterated logarithm Sequential test Asset returns
AMS 2000 Subject ClassificationPrimary 62G32 Secondary 62G05, 62G20
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