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Estimating the Hurst effect and its application in monitoring clinical trials. (English) Zbl 1429.62559

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.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
60G22 Fractional processes, including fractional Brownian motion
62M09 Non-Markovian processes: estimation
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