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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 Gourieroux et al. (1984) 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 [Authors]

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The dispersal pattern of the sand fly Lutzomyia neivai was studied through mark-release-recapture experiments in an American cutaneous leishmaniasis endemic rural area in Southeastern Brazil. Over 6500 specimens were marked with fluorescent powder and released in forest edge and peridomicile habitats from August to November 1999, February and April 2000. Recapture attempts were made using Shannon and CDC traps up to eight successive nights after releases. A total of 493 (7.58%) specimens were recaptured. The number of recaptured males and females of L. neivai in CDC traps was not affected by the distance between the trap and the release points. Approximately 90% of males and females recaptured in CDC traps were caught up to 70 m from the release points. The maximum female flight range recorded was 128 m. The average flight range per day was less than 60 m for males and females. Of the flies released in forest edge, approximately 16% of the recaptured females were caught in Shannon traps in the peridomicile habitat. The results indicate that the movements of L. neivai are spatially focal and the possibility of dispersion from forest to peridomicile habitat may be an important way of contracting leishmaniasis in dwellings.