Perturbation selection and influence measures in local influence analysis

Cook's [J. Roy. Statist. Soc. Ser. B 48 (1986) 133--169] local influence approach based on normal curvature is an important diagnostic tool for assessing local influence of minor perturbations to a statistical model. However, no rigorous approach has been developed to address two fundamental issues: the selection of an appropriate perturbation and the development of influence measures for objective functions at a point with a nonzero first derivative. The aim of this paper is to develop a differential--geometrical framework of a perturbation model (called the perturbation manifold) and utilize associated metric tensor and affine curvatures to resolve these issues. We will show that the metric tensor of the perturbation manifold provides important information about selecting an appropriate perturbation of a model. Moreover, we will introduce new influence measures that are applicable to objective functions at any point. Examples including linear regression models and linear mixed models are examined to demonstrate the effectiveness of using new influence measures for the identification of influential observations.Comment: Published in at http://dx.doi.org/10.1214/009053607000000343 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Structure and chemistry of Orion S

We present interferometric observations of the SiO J = 2-1, H^(13)CO^+ J = 1-0, HC_3N J = 11-10, CH_3OH J_K = 2_0-1_0, and SO_2 J(K_pK_0) = 8_(17)-8_(08) transitions along with the λ = 3.1 mm continuum toward the young stellar object Orion S. The HC_3N and H^(13)CO^+ emission trace similar spatial and velocity distributions which are extended and follow the Orion molecular ridge. The SiO emission is more spatially confined, peaking to the west of the λ = 3.1 mm continuum source, while the CH_3OH emission peaks to the southwest. Weak SO_2 emission was detected southeast of the continuum source position. Column densities and fractional abundances are derived for each species at different positions in the region. In general, the molecular abundances near the continuum source are similar to those in the quiescent material near IRc 2, but the abundances decrease toward the continuum source position indicating localized depletions of at least a factor of three. The presence of strong SiO emission with much weaker SO_2 emission is interpreted as resulting from high-velocity shock interactions between the outflow from Orion S and the surrounding cloud. The apparent molecular depletions directly toward Orion S, and the similarity of abundances between the Orion S region and quiescent ridge material, suggest that Orion S is at an early stage of chemical evolution, prior to when substantial chemical differentiation occurs