Simultaneous confidence intervals for comparisons of several multinomial samples

Simultaneous confidence intervals from randomization tests with application in testing bioequivalence with multiple endpoints

We propose a method to construct simultaneous confidence intervals for a parameter vector from inverting a series of randomization tests (RT). The randomization tests are facilitated by an efficient multivariate Robbins-Monro procedure that takes the correlation information of all components into account. The estimation method does not require any distributional assumption of the population other than the existence of the second moments. The resulting simultaneous confidence intervals are not necessarily symmetric about the point estimate of the parameter vector but possess the property of equal tails in all dimensions. In particular, we present the constructing the mean vector of one population and the difference between two mean vectors of two populations. Extensive simulation is conducted to show numerical comparison with four methods. We illustrate the application of the proposed method to test bioequivalence with multiple endpoints on some real data.

Distance assessment of detours by jumping spiders

To take an indirect route (detour) in order to reach a specific target requires complex cognitive processes. Yet more demanding, from the cognitive point of view, is when the goal is only visible at the beginning of the detour. In spiders from the family Salticidae, vision is a key sensory modality mediating navigation and prey search. Their acute vision allows them to perform complicated detours, possibly as a consequence of the multitude of potential routes in their typically complex 3-dimensional habitats. We used a 4-route choice test, in which routes differed in being either short or long and in the presence or absence of a lure of a prey item, to investigate route assessment in 2 salticid species, Trite planiceps and Marpissa marina. Although both species showed evidence of motivation to follow lured-routes, judging by the number of times they re-oriented toward them while detouring, we found that Trite chose short routes in preference to long routes, but did not prefer the lured-routes. In contrast, Marpissa exhibited random route choice, although it oriented toward lured-routes more often than control routes (lure absent). Our results suggest that decision-making processes about which route to take occurs before embarking on a route, but this is cognitively challenging. Spiders exhibited cognitive limitations in which the lack of visibility of the goal affected success. However, the severity of cognitive limitations depended on species. We suggest that variability in spatial ability across the Salticidae may be related to the habitat complexity inhabited by each species.