Maximum Likelihood Drift Estimation for Gaussian Process with Stationary Increments
| Autor: | Yuliya Mishura, Kostiantyn Ralchenko, Sergiy Shklyar |
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| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Austrian Journal of Statistics, Vol 46, Iss 3-4 (2017) |
| Druh dokumentu: | article |
| ISSN: | 1026-597X 59540419 |
| DOI: | 10.17713/ajs.v46i3-4.672 |
| Popis: | The paper deals with the regression model X_t = \theta t + B_t , t\in[0, T ], where B=\{B_t, t\geq 0\} is a centered Gaussian process with stationary increments. We study the estimation of the unknown parameter $\theta$ and establish the formula for the likelihood function in terms of a solution to an integral equation. Then we find the maximum likelihood estimator and prove its strong consistency. The results obtained generalize the known results for fractional and mixed fractional Brownian motion. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
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