Parameter Estimation in Linear Filtering
NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS
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Suppose on a probability space omega, F, P a partially observable random process x sub l, Y sub 1, t or 0 is given where only the second component y sub 1 is observed. Furthermore assume that x sub 1, y sub 1 satisfy a certain system of stochastic differential equations driven by independent Wiener processes W sub 1 t and W 2 sub 2. We obtain a large deviation inequality for the maximum likelihood estimator m.l.e. of the unknown parameter theta alpha, beta. This inequality enables us to prove the strong consistency, asymptotic normality and covergence of the moments of the m. l.e. The method of proof can be extended to obtain similar results when multi- dimensional instead of one dimensional processes are considered and theta is a k-dimensional vector.
- Statistics and Probability