On partial local smoothing rules for curve estimation

We compare the performances of local and global rules for smoothingparameter choice, in terms of asymptotic mean squared errorsof the resulting estimators. In some instances there is surprisinglylittle to choose between local and global approaches; our analysisidentifies contexts where the differences are small or large.This work motivates development of smoothing rules that forma ‘half-way house’ between local and global smoothing.There, interpolation provides a basis for partial local smoothing.A key result shows that interpolation on even a coarse gridcan produce a very good approximation to full local smoothing.Our theoretical and numerical results lead us to suggest linearinterpolation of a bandwidth obtained by integral approximationson discrete intervals.     

Two-stage functional mixed models for evaluating the effect of longitudinal covariate profiles on a scalar outcome

The Daily Hormone Study, a substudy of the Study of Women's Health Across the Nation (SWAN) consisting of more than 600 pre- and perimenopausal women, includes a scalar measure of total hip bone mineral density (BMD) together with repeated measures of creatinine-adjusted follicle stimulating hormone (FSH) assayed from daily urine samples collected over one menstrual cycle. It is of scientific interest to investigate the effect of the FSH time profile during a menstrual cycle on total hip BMD, adjusting for age and body mass index. The statistical analysis is challenged by several features of the data: (1) the covariate FSH is measured longitudinally and its effect on the scalar outcome BMD may be complex; (2) due to varying menstrual cycle lengths, subjects have unbalanced longitudinal measures of FSH; and (3) the longitudinal measures of FSH are subject to considerable among- and within-subject variations and measurement errors. We propose a measurement error partial functional linear model, where repeated measures of FSH are modeled using a functional mixed effects model and the effect of the FSH time profile on BMD is modeled using a partial functional linear model by treating the unobserved true subject-specific FSH time profile as a functional covariate. We develop a two-stage nonparametric regression calibration method using period smoothing splines. Using the connection between smoothing splines and mixed models, we show that a key feature of our approach is that estimation at both stages can be conveniently cast into a unified mixed model framework. A simple testing procedure for constant functional covariate effect is also proposed. The proposed methods are evaluated using simulation studies and applied to the SWAN data.     

Reducing variability of crossvalidation for smoothing-parameter choice

One of the attractions of crossvalidation, as a tool for smoothing-parameterchoice, is its applicability to a wide variety of estimatortypes and contexts. However, its detractors comment adverselyon the relatively high variance of crossvalidatory smoothingparameters, noting that this compromises the performance ofthe estimators in which those parameters are used. We show thatthe variability can be reduced simply, significantly and reliablyby employing bootstrap aggregation or bagging. We establishthat in theory, when bagging is implemented using an adaptivelychosen resample size, the variability of crossvalidation canbe reduced by an order of magnitude. However, it is arguablymore attractive to use a simpler approach, based for exampleon half-sample bagging, which can reduce variability by approximately50%.     

The effects of interpolation error and location quality on animal track reconstruction

The Global Positioning System (GPS) gives precise estimates of location. However, the investigation of animal movement and behavior often requires interpolation to examine events between such fixes. We obtained 6,288 GPS locations from an electronic tag deployed for 170 d on an adult male gray seal ( Halichoerus grypus ) that ranged freely off the east coast of Scotland, and interpolated between subsamples of these data to investigate the growth of uncertainty within the intervals between observations. Average uncertainty over the path increased linearly as the interval between interpolating locations increased, reaching 12 km in longitude and 6 km in latitude at 2-d separation. The decrease in precision caused by duty-cycling, only collecting data in part of the day, was demonstrated. Adding noise to the GPS locations to simulate data from the ARGOS satellite system had little effect on the total errors for observations separated by more than 12 h. While the rate of growth in interpolation error is likely to vary between species, these results suggest that frequent, and preferably evenly spaced, location fixes are required to take full advantage of the precision of GPS data in the reconstruction of animal tracks.     

全球陆地保护地60年增长情况分析和趋势预测

保护地建设已成为全球生物多样性保护的第一道防线。掌握其在不同尺度上的发展状况和变化趋势对保护地规划和建设有重要意义。针对已有研究在时间跨度、空间尺度以及结果对比方面的不足, 本文基于世界保护地数据库(World Database of Protected Areas, http://www.protectedplanet.net), 对全球、洲际、地区及国家尺度1950-2013年陆地保护地的增长情况进行描述和短期预测。结果发现: (1)全球保护地增长速率不断加快, 特别是在20世纪90年代以后。(2)洲际和地区保护地发展大致呈现3种增长趋势: 在美洲及大洋洲, 多数地区的保护地增长速率一直在加快; 在亚洲和欧洲, 多数地区的发展高峰出现在20世纪80、90年代; 在非洲, 多数地区的发展高峰为20世纪70年代及21世纪前10年。(3)各国保护地建设存在不平衡性, 仍有近一半国家的陆地保护地比例小于10%, 但这种差距随时间的推移有缩小的趋势。(4)绝大部分保护地增速均匀性低的国家分布在非洲。(5)虽然全球的《爱知生物多样性目标》在2020年预计不能完成, 但包括中国在内的22个国家有望如期达到目标。本文结果为未来保护地规划和建设工作的开展提供了参考依据。     

Bayesian semiparametric intensity estimation for inhomogeneous spatial point processes

In this work we propose a fully Bayesian semiparametric method to estimate the intensity of an inhomogeneous spatial point process. The basic idea is to first convert intensity estimation into a Poisson regression setting via binning data points on a regular grid, and then model the log intensity semiparametrically using an adaptive version of Gaussian Markov random fields to smooth the corresponding counts. The inference is carried by an efficient Markov chain Monte Carlo simulation algorithm. Compared to existing methods for intensity estimation, for example, parametric modeling and kernel smoothing, the proposed estimator not only provides inference regarding the dependence of the intensity function on possible covariates, but also uses information from the data to adaptively determine the amount of smoothing at the local level. The effectiveness of using our method is demonstrated through simulation studies and an application to a rainforest dataset.