Parameter estimation for one-sided heavy-tailed distributions
| Autor: | Phillip Kerger, Kei Kobayashi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
2010: 62F10 60G52 62F12 Estimation theory Probability (math.PR) 010102 general mathematics Estimator Mathematics - Statistics Theory Statistics Theory (math.ST) 01 natural sciences Power law 010104 statistics & probability One sided Fixed time FOS: Mathematics Statistical physics 0101 mathematics Statistics Probability and Uncertainty Mathematics - Probability Mathematics |
| Popis: | Stable subordinators, and more general subordinators possessing power law probability tails, have been widely used in the context of subdiffusions, where particles get trapped or immobile in a number of time periods, called constant periods. The lengths of the constant periods follow a one-sided distribution which involves a parameter between 0 and 1 and whose first moment does not exist. This paper constructs an estimator for the parameter, applying the method of moments to the number of observed constant periods in a fixed time interval. The resulting estimator is asymptotically unbiased and consistent, and it is well-suited for situations where multiple observations of the same subdiffusion process are available. We present supporting numerical examples and an application to market price data for a low-volume stock. 13 pages, 7 figures, to appear in Statistics & Probability Letters |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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