Maximum likelihood estimation in linear infinite dimensional models
Mohapl, Jaroslav; Mohapl, Jaroslav; Department of statistics and actuarial science, University of Waterloo
Журнал:
Communications in Statistics. Stochastic Models
Дата:
1994
Аннотация:
Consider a martingale with values in the strong dual of a nuclear space . Let c(t) satisfy the functional equation in which valued Gaussian white noise process and with , are continuous linear operators. It is shown that under suitable assumptions the initial condition c(0) can be chosen in such a way that becomes an ergodic stationary Markov process and the unknown parameter θcan be estimated by the maximum likelihood method. The obtained estimator of θis strongly consistent and satisfies a version of the central limit theorem
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