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Fourth order pseudo maximum likelihood methods. (English) Zbl 1441.62733
Summary: We extend PML theory to account for information on the conditional moments up to order four, but without assuming a parametric model, to avoid a risk of misspecification of the conditional distribution. The key statistical tool is the quartic exponential family, which allows us to generalize the PML2 and QGPML1 methods proposed in [C. Gourieroux et al., Econometrica 52, 681–700 (1984; Zbl 0575.62031)] to PML4 and QGPML2 methods, respectively. An asymptotic theory is developed. The key numerical tool that we use is the Gauss-Freud integration scheme that solves a computational problem that has previously been raised in several fields. Simulation exercises demonstrate the feasibility and robustness of the methods.

##### MSC:
 62P20 Applications of statistics to economics
nlmdl; OPQ
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##### References:
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