On the exact maximum likelihood estimation of Gaussian autoregressive processes

1988 ◽  
Vol 36 (6) ◽  
pp. 922-924 ◽  
Author(s):  
B. Cernuschi-Frias ◽  
J.D. Rogers
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Autoregressive Processes ◽  
Exact Maximum Likelihood

Maximum likelihood estimation for stochastic rth-order reactions. II

1973 ◽  
Vol 10 (02) ◽  
pp. 441-446
Author(s):  
John P. Mullooly
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Waiting Time ◽  
Likelihood Estimation ◽  
Initial Number ◽  
Asymptotically Normal ◽  
Reaction Event ◽  
Wide Range ◽  
Order Case ◽  
Exact Maximum Likelihood

In this paper we consider maximum likelihood estimation of the rate constant for stochastic rth-order reactions based on observation of the level of the system at time t > 0. Conditions are found for which the waiting time until the nth. reaction event is asymptotically normal, as the initial number of molecules and the number of reaction events become large. This distributional result is used to derive an approximate estimator which is shown for the second-order case to be close to the exact maximum likelihood estimate over a wide range of percentage completion.

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