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Analyse asymptotique des processus autorégressifs de bifurcation par des méthodes de martingales.
| Content Provider | Semantic Scholar |
|---|---|
| Author | Gégout-Petit, Anne Saporta, Benoîte De Bercu, Bernard |
| Copyright Year | 2008 |
| Abstract | We study the least-square (LS) estimator of the unknown parameters of a bifurcating auto-regressive process (BAR). Under very weak assumptions on the noise sequence (namely conditional pair-wise independence and moments of order $4$), we derive a precise rate of convergence for the LS estimator, as well as a quadratic strong law and a central limit theorem. Our main tool is martingale theory. However, standard results do not apply directly, as the martingales involved here have a special form and an exponential growth rate. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://imag.umontpellier.fr/~saporta/PDF/EXPOSES/Lille01-2009.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
