Abstract
Frequently, corresponding to a given estimating equation it would be desirable to have a scalar combinant having parametric derivative equal to the estimating function since such a combinant may serve as a quasi log likelihood. In general this cannot be achieved but it is nevertheless possible to define a quasi profile log likelihood and also a quasi directed likelihood, for an arbitrary one-dimensional parameter of interest and with the standard kind of distributional limit behaviour.
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Barndorff-Nielsen, O.E. Quasi profile and directed likelihoods from estimating functions. Ann Inst Stat Math 47, 461–464 (1995). https://doi.org/10.1007/BF00773395
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DOI: https://doi.org/10.1007/BF00773395