Distributed Estimator of Market Beta under Extreme Conditions

Market beta is a measure of the volatility or systematic risk of a security or portfolio compared to the market as a whole. This paper considers the distributed estimation of market beta in the case of massive data, and obtains the consistency and asymptotic normality of the estimator. Further, simulations show the finite sample properties of this estimator.

A multi-scale modelling framework to guide management of plant invasions in a transboundary context

Background：Attention has recently been drawn to the issue of transboundary invasions,where species introduced and naturalized in one country cross international borders and become problematic in neighbouring countries.Robust modelling frameworks,able to identify the environmental drivers of invasion and forecast the current and future potential distribution of invasive species,are needed to study and manage invasions.Limitations due to the lack of species distribution and environmental data,or assumptions of modelling tools,often constrain the reliability of model predictions.Methods：We present a multiscale spatial modelling framework for transboundary invasions,incorporating robust modelling frameworks（Multimodel Inference and Ensemble Modelling） to overcome some of the limitations.The framework is illustrated using Hakea sericea Schrad.（Proteaceae）,a shrub or small tree native to Australia and invasive in several regions of the world,including the Iberian Peninsula.Two study scales were considered：regional scale（western Iberia,including mainland Portugal and Galicia） and local scale（northwest Portugal）.At the regional scale,the relative importance of environmental predictors sets was evaluated and ranked to determine the main general drivers for the species distribution,while the importance of each environmental predictor was assessed at the local scale.The potential distribution of H.sericea was spatially projected for both scale areas.Results：Model projections for western Iberia suggest that a large area is environmentally suitable in both Portugal and Spain.Climate and landscape composition sets were the most important determinants of this regional distribution of the species.Conversely,a geological predictor（schist lithology） was more important in explaining its local-scale distribution.Conclusions：After being introduced to Portugal,H.sericea has become a transboundary invader by expanding in parts of Galicia（Spain）.The fact that a larger area is predicted as environmentally suitable in Spain raises concerns regarding its potential continued expansion.This highlights the importance of transboundary cooperation in the early management of invasions.By reliably identifying drivers and providing spatial projections of invasion at multiple scales,this framework provides insights for the study and management of biological invasions,including the assessment of transboundary invasion risk.