Statistics Department Seminar Series: Frederi Viens, Professor, Department of Statistics and Probability, Michigan State University
"Parameter estimation and testing in long-memory and other Gaussian and second-chaos processes"
Abstrtact: We consider the class of all stationary Gaussian processes. When the spectral density is parametrically explicit, we define a Generalized Method of Moments estimator that satisfies consistency and asymptotic normality, using the Breuer-Major theorem which applies to long-memory processes. This result is applied to the joint estimation of the three parameters of a stationary fractional Ornstein-Uhlenbeck (fOU) process driven for all Hurst parameters. For general processes observed at fixed discrete times, no matter what the memory length, we use state-of-the-art Malliavin calculus tools to prove BerryEsseen-type and other speeds of convergence in total variation, for estimators based on power variations. This is joint work with Luis Barboza (U. Costa Rica), Khalifa es-Sebaiy (U. Kuwait), and Soukaina Douissi (U. Cadi Ayyad, Morocco). Time permitting, we will reveal some ideas from ongoing work with Fatimah Alsharani (MSU) and Philip Ernst (Rice U., Houston, Texas) on hypothesis testing for Gaussian processes extending modeling to second-chaos processes, with applications to sea-level rise.
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