Power properties if invariant tests for spatial autocorrelation in linear regression

This paper derives some exact power properties of tests for spatial autocorrelation in the context of a linear regression model. In particular, we characterize the circumstances in which the power vanishes as the autocorrelation increases, thus extending the work of Krämer (2005). More generally, the analysis in the paper sheds new light on how the power of tests for spatial autocorrelation is affected by the matrix of regressors and by the spatial structure. We mainly focus on the problem of residual spatial autocorrelation, in which case it is appropriate to restrict attention to the class of invariant tests, but we also consider the case when the autocorrelation is due to the presence of a spatially lagged dependent variable among the regressors. A numerical study aimed at assessing the practical relevance of the theoretical results is included

Perturbation, extraction and refinement of invariant pairs for matrix polynomials

Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of an invariant subspace needs to be replaced by the concept of an invariant pair. Little has been known so far about numerical aspects of such invariant pairs. The aim of this paper is to fill this gap. The behavior of invariant pairs under perturbations of the matrix polynomial is studied and a first-order perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly based on the polynomial formulation. Numerical experiments with matrix polynomials from a number of applications demonstrate the effectiveness of our extraction and refinement procedures.

Early identification of stimulant treatment responders, partial responders and non-responders using objective measures in children and adolescents with hyperkinetic disorder

Background: The aim of this study was to evaluate stimulant medication response following a single dose of methylphenidate (MPH) in children and young people with hyperkinetic disorder using infrared motion analysis combined with a continuous performance task (QbTest system) as objective measures. The hypothesis was put forward that a moderate testdose of stimulant medication could determine a robust treatment response, partial response and non-response in relation to activity, attention and impulse control measures. Methods: The study included 44 children and young people between the ages of 7-18 years with a diagnosis of hyperkinetic disorder (F90 & F90.1). A single dose-protocol incorporated the time course effects of both immediate release MPH and extended release MPH (Concerta XL, Equasym XL) to determine comparable peak efficacy periods post intake. Results: A robust treatment response with objective measures reverting to the population mean was found in 37 participants (84%). Three participants (7%) demonstrated a partial response to MPH and four participants (9%) were determined as non-responders due to deteriorating activity measures together with no improvements in attention and impulse control measures. Conclusion: Objective measures provide early into prescribing the opportunity to measure treatment response and monitor adverse reactions to stimulant medication. Most treatment responders demonstrated an effective response to MPH on a moderate testdose facilitating a swift and more optimal titration process.

Multiple diversity measures to identify complementary conservation areas for the Baja California peninsular cacti

The Baja California Peninsula is home to 85 species of cacti, of which 54 are endemic, highlighting its importance as a cactus diverse region within Mexico. Many species are under threat due to collection pressure and habitat loss, but ensuring maximal protection of cacti species requires a better understanding of diversity patterns. We assessed species richness, endemism, and phylogenetic and morphological diversity using herbarium records and a molecular phylogeny for 82 species of cacti found in the peninsula. The four diversity measures were estimated for the existing nature reserve network and for 314 hexagrids of 726 km2. Using the hexagrid data, we surveyed our results for areas that best complement the current protected cacti diversity in the Baja California Peninsula. Currently, the natural reserve network in Baja shelters an important amount of the cacti diversity (74% of the species, 85.9% of the phylogenetic diversity, 76% of endemics and all the growth forms). While species richness produced several solutions to complement the diversity protected, by identifying priority species (endemic species with high contribution to overall PD) one best solution is reported. Three areas (San Matías, Magdalena and Margarita Islands and El Triunfo), selected using species richness, PD and endemism, best complement the diversity currently protected, increasing species richness to 89%, PD to 94% and endemism to 89%, and should be considered in future conservation plans. Two of these areas could be included within nature reserves already established.

Corporate social performance and stock returns: UK evidence from disaggregate measures

This study examines the relation between corporate social performance and stock returns in the UK. We closely evaluate the interactions between social and financial performance with a set of disaggregated social performance indicators for environment, employment, and community activities instead of using an aggregate measure. While scores on a composite social performance indicator are negatively related to stock returns, we find the poor financial reward offered by such firms is attributable to their good social performance on the environment and, to a lesser extent, the community aspects. Considerable abnormal returns are available from holding a portfolio of the socially least desirable stocks. These relationships between social and financial performance can be rationalized by multi-factor models for explaining the cross-sectional variation in returns, but not by industry effects.

Different risk measures: different portfolio compositions?

Traditionally, the measure of risk used in portfolio optimisation models is the variance. However, alternative measures of risk have many theoretical and practical advantages and it is peculiar therefore that they are not used more frequently. This may be because of the difficulty in deciding which measure of risk is best and any attempt to compare different risk measures may be a futile exercise until a common risk measure can be identified. To overcome this, another approach is considered, comparing the portfolio holdings produced by different risk measures, rather than the risk return trade-off. In this way we can see whether the risk measures used produce asset allocations that are essentially the same or very different. The results indicate that the portfolio compositions produced by different risk measures vary quite markedly from measure to measure. These findings have a practical consequence for the investor or fund manager because they suggest that the choice of model depends very much on the individual’s attitude to risk rather than any theoretical and/or practical advantages of one model over another.

The impact of news on measures of undiversifiable risk: evidence from the UK stock market

Using UK equity index data, this paper considers the impact of news on time varying measures of beta, the usual measure of undiversifiable risk. The empirical model implies that beta depends on news about the market and news about the sector. The asymmetric response of beta to news about the market is consistent across all sectors considered. Recent research is divided as to whether abnormalities in equity returns arise from changes in expected returns in an efficient market or over-reactions to new information. The evidence suggests that such abnormalities may be due to changes in expected returns caused by time-variation and asymmetry in beta.

Connectivity measures for internet topologies on the level of autonomous systems

Classical measures of network connectivity are the number of disjoint paths between a pair of nodes and the size of a minimum cut. For standard graphs, these measures can be computed efficiently using network flow techniques. However, in the Internet on the level of autonomous systems (ASs), referred to as AS-level Internet, routing policies impose restrictions on the paths that traffic can take in the network. These restrictions can be captured by the valley-free path model, which assumes a special directed graph model in which edge types represent relationships between ASs. We consider the adaptation of the classical connectivity measures to the valley-free path model, where it is -hard to compute them. Our first main contribution consists of presenting algorithms for the computation of disjoint paths, and minimum cuts, in the valley-free path model. These algorithms are useful for ASs that want to evaluate different options for selecting upstream providers to improve the robustness of their connection to the Internet. Our second main contribution is an experimental evaluation of our algorithms on four types of directed graph models of the AS-level Internet produced by different inference algorithms. Most importantly, the evaluation shows that our algorithms are able to compute optimal solutions to instances of realistic size of the connectivity problems in the valley-free path model in reasonable time. Furthermore, our experimental results provide information about the characteristics of the directed graph models of the AS-level Internet produced by different inference algorithms. It turns out that (i) we can quantify the difference between the undirected AS-level topology and the directed graph models with respect to fundamental connectivity measures, and (ii) the different inference algorithms yield topologies that are similar with respect to connectivity and are different with respect to the types of paths that exist between pairs of ASs.