Existence of Maximum Likelihood Estimates in Regression Models for Grouped and Ungrouped Data

In general, concavity of the log likelihood alone does not imply that the MLE exists always. For a class of linear regression models for grouped and ungrouped data, a necessary and sufficient condition is obtained for the existence of the maximum likelihood estimator. This condition has an intuitive...

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Bibliographic Details
Published in:Journal of the Royal Statistical Society. Series B, Methodological Methodological, 1986-01, Vol.48 (1), p.100-106
Main Authors: Silvapulle, M. J., Burridge, J.
Format: Article
Language:English
Subjects:
Censored data
Data models
Exact sciences and technology
existence
grouped and ungrouped data
Hyperplanes
Linear models
Linear programming
Linear regression
Mathematics
Maximum likelihood estimation
maximum likelihood estimator
Maximum likelihood estimators
Parametric inference
Probability and statistics
proportional hazards
regression
Regression analysis
Sciences and techniques of general use
Statistics
Sufficient conditions
uniqueness
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Summary:In general, concavity of the log likelihood alone does not imply that the MLE exists always. For a class of linear regression models for grouped and ungrouped data, a necessary and sufficient condition is obtained for the existence of the maximum likelihood estimator. This condition has an intuitively simple interpretation. Further, it turns out that there are similar necessary and sufficient conditions for the existence of maximum likelihood estimates for a number of other non-linear models such as Cox's Regression Model. For a given set of data, these conditions may be verified by Linear Programming Methods.
ISSN:0035-9246
1369-7412
2517-6161
1467-9868
DOI:10.1111/j.2517-6161.1986.tb01394.x