Brownian distance covariance

Distance correlation is a new class of multivariate dependence coefficients applicable to random vectors of arbitrary and not necessarily equal dimension. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but generalize and extend these classical bivariate measures of dependence. Distance correlation characterizes independence: it is zero if and only if the random vectors are independent. The notion of covariance with respect to a stochastic process is introduced, and it is shown that population distance covariance coincides with the covariance with respect to Brownian motion; thus, both can be called Brownian distance covariance. In the bivariate case, Brownian covariance is the natural extension of product-moment covariance, as we obtain Pearson product-moment covariance by replacing the Brownian motion in the definition with identity. The corresponding statistic has an elegantly simple computing formula. Advantages of applying Brownian covariance and correlation vs the classical Pearson covariance and correlation are discussed and illustrated.Comment: This paper discussed in: [arXiv:0912.3295], [arXiv:1010.0822], [arXiv:1010.0825], [arXiv:1010.0828], [arXiv:1010.0836], [arXiv:1010.0838], [arXiv:1010.0839]. Rejoinder at [arXiv:1010.0844]. Published in at http://dx.doi.org/10.1214/09-AOAS312 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

DISCO analysis: A nonparametric extension of analysis of variance

In classical analysis of variance, dispersion is measured by considering squared distances of sample elements from the sample mean. We consider a measure of dispersion for univariate or multivariate response based on all pairwise distances between-sample elements, and derive an analogous distance components (DISCO) decomposition for powers of distance in $(0,2]$. The ANOVA F statistic is obtained when the index (exponent) is 2. For each index in $(0,2)$, this decomposition determines a nonparametric test for the multi-sample hypothesis of equal distributions that is statistically consistent against general alternatives.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS245 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Role of spontaneous plants as a reservoir of alternative hosts for Semielacher petiolatus (Girault) and Citrostichus phyllocnistoides (Narayanan) (Hymenoptera, Eulophidae) in citrus groves

The role spontaneous plants could eventually play towards populations of two exotic parasitoids, Semielacher petiolatus (Girault) and Citrostichus phyllocnistoides (Narayanan), was investigated in five Sicilian citrus groves. Both species were obtained from two herbs typically living beneath the citrus trees in the period of scarce availability of P. citrella larvae on citrus plants, and precisely: S. petiolatus was reared from Cosmopterix pulcherimella Chambers, leafminer on Parietaria diffusa M. et K., while C. phyllocnistoides on the same species and on a Liriomyza species associated to Mercurialis annua L., these last two host records being new for the parasitoid. Vegetational diversity can then enhance survival and maintenance of populations of exotic parasitoids in citrus agroecosystem, providing them with alternative hosts. The incidence of parasitism of S. petiolatus and C. phyllocnistoides on non-target hosts was, however, so low (2.8% for S. petiolatus on C. pulcherimella, and 8.3% and 3.3% for C. phyllocnistoides on C. pulcherimella and Liriomyza sp. respectively) that a negative impact on both native leafminer and autochthonous parasitoid populations can be excluded

Measuring and testing dependence by correlation of distances

Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation, distance correlation is zero only if the random vectors are independent. The empirical distance dependence measures are based on certain Euclidean distances between sample elements rather than sample moments, yet have a compact representation analogous to the classical covariance and correlation. Asymptotic properties and applications in testing independence are discussed. Implementation of the test and Monte Carlo results are also presented.Comment: Published in at http://dx.doi.org/10.1214/009053607000000505 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Hymenoptera Chalcidoidea inhabiting galls of Cynipidae in Jordan

Twenty-three species of Chalcidoidea (5 Eurytomidae, 4 Torymidae, 2 Ormyridae, 5 Pteromalidae and 7 Eulophidae) are recorded as regular members of the parasitoid fauna inhabiting galls of Cynipidae in Jordan. The occurrence of three additional species, probably only facultatively associated with cynipid galls, is noted. Twenty-two out of the total 26 species were previously unrecorded in the country, while 13 of them are also new for the entire Middle East. Eighteen new host records were detected, together with 24 new plant-parasitoid associations. The biology of each species is briefly commented upon, as well as the presence of a host-related colour variation in some species