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Maximum Likelihood Estimation, Nonregular


  1. David M. Holland

Published Online: 15 SEP 2006

DOI: 10.1002/9780470057339.vam009m

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Holland, D. M. 2006. Maximum Likelihood Estimation, Nonregular. Encyclopedia of Environmetrics. 4.

Author Information

  1. United States Environmental Protection Agency, NC, USA

Publication History

  1. Published Online: 15 SEP 2006


For bounded probability distributions capable of J or U shapes, the log-likelihood function can become unbounded as the boundary parameters approach their respective limits. However, use of penalty function techniques that urge the maximum likelihood (ML) search away from the unbounded region can be used to circumvent this problem. Another approach to nonregular problems is ‘correcting’ the likelihood to estimate the model parameters. In an application to simulated data, this technique was found to be effective with quick convergence to parameter estimates.


  • maximum likelihood;
  • nonregular estimation;
  • probability distribution