Using semiparametric‐mixed model and functional linear model to detect vulnerable prenatal window to carcinogenic polycyclic aromatic hydrocarbons on fetal growth

Prenatal exposure to carcinogenic polycyclic aromatic hydrocarbons (c‐PAHs) through maternal inhalation induces higher risk for a wide range of fetotoxic effects. However, the most health‐relevant dose function from chronic gestational exposure remains unclear. Whether there is a gestational window during which the human embryo/fetus is particularly vulnerable to PAHs has not been examined thoroughly. We consider a longitudinal semiparametric‐mixed effect model to characterize the individual prenatal PAH exposure trajectory, where a nonparametric cyclic smooth function plus a linear function are used to model the time effect and random effects are used to account for the within‐subject correlation. We propose a penalized least squares approach to estimate the parametric regression coefficients and the nonparametric function of time. The smoothing parameter and variance components are selected using the generalized cross‐validation (GCV) criteria. The estimated subject‐specific trajectory of prenatal exposure is linked to the birth outcomes through a set of functional linear models, where the coefficient of log PAH exposure is a fully nonparametric function of gestational age. This allows the effect of PAH exposure on each birth outcome to vary at different gestational ages, and the window associated with significant adverse effect is identified as a vulnerable prenatal window to PAHs on fetal growth. We minimize the penalized sum of squared errors using a spline‐based expansion of the nonparametric coefficient function to draw statistical inferences, and the smoothing parameter is chosen through GCV.     

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.     

Multidimensional adaptive P-splines with application to neurons' activity studies

The receptive field (RF) of a visual neuron is the region of the space that elicits neuronal responses. It can be mapped using different techniques that allow inferring its spatial and temporal properties. Raw RF maps (RFmaps) are usually noisy, making it difficult to obtain and study important features of the RF. A possible solution is to smooth them using P-splines. Yet, raw RFmaps are characterized by sharp transitions in both space and time. Their analysis thus asks for spatiotemporal adaptive P-spline models, where smoothness can be locally adapted to the data. However, the literature lacks proposals for adaptive P-splines in more than two dimensions. Furthermore, the extra flexibility afforded by adaptive P-spline models is obtained at the cost of a high computational burden, especially in a multidimensional setting. To fill these gaps, this work presents a novel anisotropic locally adaptive P-spline model in two (e.g., space) and three (space and time) dimensions. Estimation is based on the recently proposed SOP (Separation of Overlapping Precision matrices) method, which provides the speed we look for. Besides the spatiotemporal analysis of the neuronal activity data that motivated this work, the practical performance of the proposal is evaluated through simulations, and comparisons with alternative methods are reported.     

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.