\noindent We introduce new estimates and tests of independence in copula models with unknown margins using ϕ-divergences and the duality technique. The asymptotic laws of the estimates and the test statistics are established both when the parameter is an interior or a boundary value of the parameter space. Simulation results show that the choice of χ2-divergence has good properties in terms of efficiency-robustness.
The life cycle of Hedruris spinigera Baylis, 1931 (Nematoda: Hedruridae) is determined here with the first formal identification of the parasite's intermediate host: the crustacean amphipod Paracorophium excavatum Thomson. Adult H. spinigera are redescribed from specimens collected from the stomach of fishes, Retropinna retropinna (Richardson) and Aldrichetta forsteri (Valenciennes), from Lake Waihola, New Zealand. Immature adults of the parasite collected from intermediate hosts (P. excavatum) are also described for the first time. The prevalence, abundance and intensity of infection of H. spinigera in several fish species are quantified along with the occurrence of P. excavatum, the parasite's intermediate host, in fish stomach contents. Although H. spinigera's transmission mode (trophic transmission) and fish diet potentially expose all fish species to infection, some level of host specificity must exist as parasite prevalence, abundance and intensity of infection vary greatly between potential definitive host species. We suggest here that the anatomy of the fish digestive tract and especially that of the stomach plays an important role in host suitability for H. spinigera. While P. excavatum is the only intermediate host in Lake Waihola, H. spinigera was found in six different fish species: Aldrichetta forsteri, Galaxias maculatus (Jenyns), Retropinna retropinna, Rhombosolea retiaria Hutton, Perca fluviatilis Linnaeus and Salmo trutta Linnaeus; although typical hedrurid attachment and mating positions were observed only in R. retropinna and A. forsteri. The limited distribution of H. spinigera is most likely due to that of its different host species (intermediate and definitive), all inhabitants of coastal fresh and brackish waters.
This paper is a continuation of Y. Liu, Anti-periodic solutions of nonlinear first order impulsive functional differential equations, Math. Slovaca 62 (2012), 695–720. By using Schaefer's fixed point theorem, new existence results on anti-periodic solutions of a class of nonlinear impulsive functional differential equations are established. The techniques to get the priori estimates of the possible solutions of the mentioned equations are different from those used in known papers. An example is given to illustrate the main theorems obtained. One sees easily that Example 3.1 can not be solved by Theorems 2.1–2.3 obtained in Liu's paper since (G2) in Theorem 2.1, (G4) in Theorem 2.2 and (G6) in Theorem 2.3 are not satisfied.