Maximum Likelihood Estimation of Scalar Models

  • Des F. Nicholls
  • Barry G. Quinn
Part of the Lecture Notes in Statistics book series (LNS, volume 11)


An estimation procedure is introduced in this chapter which is based on maximizing the likelihood function constructed as though the processes {ε(t)} and {B(t)} were sequences of normally distributed random variables. We shall refer to the estimates obtained in this way as maximum likelihood estimates even though it will be shown that these estimates will be strongly consistent and satisfy a central limit theorem if the processes {ε(t)} and ({B(t)} are not sequences of normally distributed random variables. It will be seen that the likelihood function to be optimized is non-linear in the parameters (to be estimated) and so it is necessary to use an iterative procedure to obtain the estimates. As was mentioned earlier, it is desirable to commence such an iterative procedure as close to the global optimum as possible in order to reduce the possibility of converging to a local optimum. For this reason we choose strongly consistent estimates of the parameters to commence the iterative procedure, such estimates having been derived in the previous chapter.


Covariance Matrix Maximum Likelihood Estimate Likelihood Function Central Limit Theorem Iterative Procedure 
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Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  • Des F. Nicholls
    • 1
  • Barry G. Quinn
    • 2
  1. 1.Australian National UniversityCanberraAustralia
  2. 2.University of WollongongWollongongAustralia

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