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Estimating the Hurst effect and its application in monitoring clinical trials. (English) Zbl 05373967
Summary: We use a direct maximum likelihood method in estimating the Hurst coefficient for fractional Brownian motion with a short length of observations. We show that the estimate is asymptotically unbiased and derive an easy to use formula for computing the variance of the estimate. We also investigate the finite sample properties via Monte Carlo simulations. The simulation studies indicate that the theoretical formulas based on large sample arguments can be used when the number of observations is relatively small. A real example for monitoring a clinical trial is used to illustrate and compare various methods.

62-99Statistics (MSC2000)
Full Text: DOI
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