Classification of Trends Via the Linear State Space Model

A method is presented for classification of trend curves based on the linear state space model. In this approach information about the smoothness of the trend curves is incorporated into the classification model by a nonstationary stochastic trend model and can thereby be used to obtain a better classification. In the case of small data sets the performance of the classification is significantly improved in comparison with the usual cluster analysis. Maximum likelihood estimation can be used to calculate the parameters of this model and to determine the classification. The classification algorithm is described in detail and the results are compared to those of the usual cluster analysis by simulation studies and by an application to tree ring data.     

Variable selection for the single-index model

We consider variable selection in the single-index model. Weprove that the popular leave-m-out crossvalidation method hasdifferent behaviour in the single-index model from that in linearregression models or nonparametric regression models. A newconsistent variable selection method, called separated crossvalidation,is proposed. Further analysis suggests that the method has betterfinite-sample performance and is computationally easier thanleave-m-out crossvalidation. Separated crossvalidation, appliedto the Swiss banknotes data and the ozone concentration data,leads to single-index models with selected variables that havebetter prediction capability than models based on all the covariates.     

The effects of fragmentation and disturbance of rainforest on ground-dwelling small mammals on the Robertson Plateau, New South Wales, Australia

We surveyed ground-dwelling small mammals in twenty-four rainforest remnants which were virtual islands surrounded by farmland on a plateau on the east coast of Australia. We investigated the effect of island size, level of disturbance, isolation and microhabitat on the abundance and species richness of the mammals. The remnants ranged from 0.3 to 29 ha, resulting from fragmentation during 175 years of European occupation. Two rodent species (Rattus fuscipes[Waterhouse, 1839] and R. rattus[Linnaeus, 1758] ) and one marsupial insectivore (Antechinus stuartii Macleay, 1841) were trapped in these remnants, with an additional species (A. swainsonii[Waterhouse, 1840] ) several kilometres away in rainforest on the escarpment of the plateau. Small-mammal species richness was low, but the native species (R. fuscipes and A. stuartii) were abundant. Three-way analyses of variance demonstrated that species richness and abundance decreased significantly with decreasing remnant size and increasing disturbance, but showed no distance effect. The abundance and richness of native species responded even more significantly. The interaction between the first two effects is important. Small remnants are affected most detrimentally by increasing disturbance, large remnants are less affected, and medium sized remnants show intermediate effects. The introduced R. rattus which was least abundant in large remnants, but more abundant in distant than near remnants, was also more abundant in those with major disturbance. The single most important variable in step-wise, multiple linear regression analyses was the logarithm of remnant area not influenced by edge effects, explaining 39% of the variance in species richness, 57% for native species richness and 46% for A. stuartii abundance. Disturbance related variables additionally contributed from 12 to 30% of the variance in dependent variables, while habitat variables explained between 22 and 48% of the variance, and accounted for two thirds of the explainable variance in R. fuscipes abundance. The implications of our results for wildlife conservation on the plateau are discussed.