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Statistical inference using maximum likelihood estimation and the generalized likelihood ratio when the true parameter is on the boundary of the parameter space

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  • Feng, Ziding
  • McCulloch, Charles E.

Abstract

The classic asymptotic properties of the maximum likelihood estimator and generalized likelihood ratio statistic do not hold when the true parameter is on the boundary of the parameter space. An inferential procedure based on an enlarged parameter space is shown to have the classical asymptotic properties. Some other competing procedures are also examined.

Suggested Citation

  • Feng, Ziding & McCulloch, Charles E., 1992. "Statistical inference using maximum likelihood estimation and the generalized likelihood ratio when the true parameter is on the boundary of the parameter space," Statistics & Probability Letters, Elsevier, vol. 13(4), pages 325-332, March.
    • Handle: RePEc:eee:stapro:v:13:y:1992:i:4:p:325-332
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    Cited by:

    1. Jodrá, P. & Jiménez-Gamero, M.D., 2016. "A note on the Log-Lindley distribution," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 189-194.
    2. Benjamin R. Saville & Amy H. Herring, 2009. "Testing Random Effects in the Linear Mixed Model Using Approximate Bayes Factors," Biometrics, The International Biometric Society, vol. 65(2), pages 369-376, June.
    3. Liu, Yin & Tian, Guo-Liang, 2015. "Type I multivariate zero-inflated Poisson distribution with applications," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 200-222.
    4. Dietz, Ekkehart & Bohning, Dankmar, 2000. "On estimation of the Poisson parameter in zero-modified Poisson models," Computational Statistics & Data Analysis, Elsevier, vol. 34(4), pages 441-459, October.
    5. Dankmar Böhning & Heinz Holling & Walailuck Böhning & Patarawan Sangnawakij, 2021. "Investigating heterogeneity in meta-analysis of studies with rare events," METRON, Springer;Sapienza Università di Roma, vol. 79(3), pages 259-272, December.
    6. Miloslavsky, Maja & van der Laan, Mark J., 2003. "Fitting of mixtures with unspecified number of components using cross validation distance estimate," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 413-428, January.
    7. Jansakul, N. & Hinde, J. P., 2002. "Score Tests for Zero-Inflated Poisson Models," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 75-96, July.
    8. Baker, Rose, 2019. "New survival distributions that quantify the gain from eliminating flawed components," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 493-501.
    9. Anders Karlström & Mårten Palme & Ingemar Svensson, 2011. "Assessing the welfare change from a pension reform," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 18(6), pages 634-657, December.

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