Recently the concept of regression depth has been introduced [1]. The deepest regression (DR) is a method for linear regression which is dened as the fit with the best depth relative to the data. In this paper we explain the properties of the DR and give some applications of deepest regression in analytical chemistry which involve regression through the origin, polynomial regression, the Michaelis-Menten model, and censored responses. 1

Exploratory Data Analysis is a widely used technique to determine which factors have the most influence on data values in a multi-way table, or which cells in the table can be considered anomalous with respect to the other cells. In particular, median polish is a simple, yet robust method to perform Exploratory Data Analysis. Median polish is resistant to holes in the table (cells that have no values), but it may require a lot of iterations through the data. This factor makes it difficult to apply median polish to large multidimensional tables, since the I/O requirements may be prohibitive. This paper describes a technique that uses median polish over an approximation of a datacube, easing the burden of I/O. The results obtained are tested for quality, using a variety of measures. The technique scales to large datacubes and proves to give a good approximation of the results that would have been obtained by median polish in the original data.

We estimated diet composition of sympatric Mexican spotted (Strix occidentalis lucida, n = 7 pairs of owls) and great horned owls (Bubo virginianus, n = 4 pairs) in ponderosa pine (Pinus ponderosa)-Gambel oak (Quercus gambelii) forest, northern Arizona. Both species preyed on mammals, birds, and insects; great horned owls also ate lizards. Mammals dominated the diet of both species. Mammals comprised 63 and 62 % of all prey items identified in diets of spotted and great horned owls, respectively, and 94 and 95 % of prey biomass. Both species primarily preyed on a few groups of small mammals. Observed overlap in diet composition between species (0.95) was greater than expected based on null models of diet overlap, and the size range of prey taken overlapped entirely. Mean prey mass was similar for both species (great horned owl, 47.0 ± 7.4 g [SE], n = 94 items; spotted owl, 40.1 ± 1.8 g, n = 1,125 items). Great horned owls consumed larger proportions of diurnally active prey than spotted owls, which primarily consumed nocturnally active mammals. Our results, coupled with a previous analysis showing that these owls foraged in the same general areas (Ganey and others 1997), suggests that they could compete for food resources, which are assumed to be limiting in at least some years. They may minimize the potential for resource competition, however, by concentrating foraging activities in different habitats (Ganey and others 1997) and by foraging at different times, when different suites of prey species are active.

Self-employment grants vs. subsidized employment: Is there a difference in the re-unemployment risk? by Kenneth Carling * and Lena Gustafson*

We propose the use of the generalized fractional Bayes factor for testing fit in multinomial models. This is a non-asymptotic method that can be used to quantify the evidence for or against a sub-model. We give expressions for the generalized fractional Bayes factor and we study its properties. In particular, we show that the generalized fractional Bayes factor has better properties than the fractional Bayes factor. Keywords: generalized fractional Bayes factor, Dirichlet process, Beta-Stacy process. 1. Introduction. In this paper we propose a Bayesian method for testing fit in multinomial models. Specifically, we will use the Bayes factor for evaluating the evidence for or against a null sub-model of the multinomial. The advantages of using a Bayesian approach for this problem are that it does not rely