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Seminar on Probability and Statistics

13:30-14:40   Room #052 (Graduate School of Math. Sci. Bldg.)
Sebastian Holtz (Humboldt University of Berlin)
Covariation estimation from noisy Gaussian observations:equivalence, efficiency and estimation
[ Abstract ]
In this work the estimation of functionals of the quadratic covariation matrix from a discretely observed Gaussian path on [0,1] under noise is discussed and analysed on a large scale. At first asymptotic equivalence in Le Cam's sense is established to link the initial high-frequency model to its continuous counterpart. Then sharp asymptotic lower bounds for a general class of parametric basic case models, including the fractional Brownian motion, are derived. These bounds are generalised to the nonparametric and even random parameter setup for certain special cases, e.g. Itô processes. Finally, regular sequences of spectral estimators are constructed that obey the derived efficiency statements.