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ARMA 过程最大似然估计量的强一致性
The strong consistency of the maximum likelihood parameter estimation method is established for multivariate Gaussian stochastic processes possessing autoregressive moving average (ARMA) representations. The demonstration in this paper exploits the ergodic theorem together with results from linear prediction theory.
有限参数随机过程族中最大似然估计一致性的一个注记
We consider families of stochastic processes indexed by a finite number of alternative parameter values. For general classes of stochastic processes it is shown that maximum likelihood estimates convergence almost surely to the correct parameter value. This established by use of a submartingale property of the sequence of maximized likelihood ratios together with a technique first employed by Wald [24] in the case of independently identically distributed random variables.