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estimate maximizes the actual log likelihood function for the data and model. The function that is maximized to form a QMLE is often a simplified form of the actual log likelihood function. A common way to form such a simplified function is to use the log-likelihood function of a misspecified model
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than the maximum likelihood estimate, but may only be slightly less efficient if the quasi-likelihood is constructed so as to minimize the loss of information relative to the actual likelihood. Standard approaches to statistical inference that are used with maximum likelihood estimates, such as the
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that treats certain data values as being independent, even when in actuality they may not be. This removes any parameters from the model that are used to characterize these dependencies. Doing this only makes sense if the dependency structure is a
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with respect to the goals of the analysis. As long as the quasi-likelihood function that is maximized is not oversimplified, the QMLE (or composite likelihood estimate) is
54:, but in discussing the consistency and (asymptotic) variance-covariance matrix, we assume some parts of the distribution may be mis-specified. In contrast, the
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formation of confidence intervals, and statistics for model comparison, can be generalized to the quasi-maximum likelihood setting.
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113:. Contemporary Mathematics. Vol. 80. Providence, RI: American Mathematical Society. pp. 221–239.
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Cox, D.R.; Reid, Nancy (2004). "A note on pseudo-likelihood constructed from marginal densities".
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that is formed by maximizing a function that is related to the logarithm of the
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Statistical inference from stochastic processes (Ithaca, NY, 1987)
254:"A note on composite likelihood inference and model selection"
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Gourieroux, Christian; Monfort, Alain; Trognon, Alain (1984).
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Lindsay, Bruce G. (1988). "Composite likelihood methods".
144:. New York, New York: Oxford University Press.
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167:"Pseudo Maximum Likelihood Methods: Theory"
140:Davidson, Russel; MacKinnon, James (2004).
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91:Partial likelihood methods for panel data
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29:quasi-maximum likelihood estimate (QMLE)
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142:Econometric Theory and Methods
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292:Maximum likelihood estimation
37:composite likelihood estimate
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33:pseudo-likelihood estimate
18:Quasi-maximum likelihood
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119:10.1090/conm/080/999014
39:, is an estimate of a
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