Background An important issue in conducting kernel home-range analyses is the choice of bandwidth or smoothing parameter. To examine the effects of this choice, telemetry data were collected at high sampling rates (843 to 5,069 locations) on 20 North American elk, Cervus elaphus, in northeastern Oregon, USA, during 2000, 2002, and 2003. The elk had their collars replaced annually, hence none were monitored for more than a single year. True home ranges were defined by buffering the actual paths of individuals. Fixed-kernel and adaptive-kernel estimates were then determined with reference bandwidths ( h ref ), least-squares cross-validation bandwidths ( h lscv ), and rule-based ad hoc bandwidths designed to prevent under-smoothing ( h ad hoc ). Both raw data and sub-sampled sparse datasets (1, 2, 4, 6, 12, and 24 locations/elk/day) were used. Results With fixed-kernel and adaptive-kernel analyses, reference bandwidths were positively biased (including areas not part of an animal’s home range) but performed better (lower bias, closer match between estimated and true home ranges) with increasing sample size. Least-squares cross-validation bandwidths were positively biased with very small sample sizes, but quickly became negatively biased with increasing sample size, as home-range estimates broke up into disjoint polygons. Ad hoc bandwidths outperformed reference and least-squares cross-validation bandwidths, exhibited only moderate positive bias, were relatively unaffected by sample size, and were characterized by lower Type I errors (falsely including areas not part of the true home range). Ad hoc bandwidths also exhibited lower Type II errors (failure to include portions of the true home range) than did least-squares cross-validation bandwidths, although reference bandwidths resulted in lowest Type II error rates. Auto-correlation indices increased to about 150 to 200 locations per elk, and then stabilized. Bias of fixed-kernel analyses with ad hoc bandwidths was not affected by auto-correlation, but did increase with irregularly shaped home ranges with high fractal dimensions. Conclusions The rule-based ad hoc bandwidths, specifically designed to prevent fragmentation of estimated home ranges, outperformed both h ref and h lscv , and gave the smallest value for h consistent with a contiguous home-range estimate. The protocol for choosing the ad hoc bandwidth was shown to be consistent and repeatable.
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机译：背景技术进行内核范围分析的一个重要问题是带宽或平滑参数的选择。为了检查此选择的效果，在2000、2002和2003年期间，以高采样率（843至5,069个位置）在美国东北俄勒冈州的20只北美麋鹿Cephus elaphus上收集了遥测数据。每年更换一次，因此没有超过一年的监测时间。真正的家庭范围是通过缓冲个人的实际路径来定义的。然后使用参考带宽（h ref ），最小二乘交叉验证带宽（h lscv ）和旨在防止平滑不足的基于规则的ad hoc带宽（h ad hoc ）。原始数据和二次采样的稀疏数据集（1、2、4、6、12和24个位置/麋鹿/天）均被使用。结果通过固定核和自适应核分析，参考带宽被正偏（包括不属于动物家园范围的区域），但随着样本量的增加，其参考带宽表现更好（偏差更低，估计的和真实的家园范围之间的匹配度更高）。最小二乘交叉验证带宽在非常小的样本量时会出现正偏，但随着家庭范围内的估计值分解为不相交的多边形，很快会随着样本量的增加而出现负偏。 Ad hoc带宽优于参考值和最小二乘交叉验证带宽，仅表现出中等正偏差，相对不受样本大小的影响，并且具有较低的I型错误（错误地包括了不属于真实归属范围的区域）的特征。尽管参考带宽导致最低的II型错误率，但ad hoc带宽也显示出比最小二乘交叉验证带宽更低的Type II错误（未能包括部分真实起始范围）。自相关指数增加到每只麋鹿约150至200个位置，然后稳定下来。具有自组织带宽的固定内核分析的偏差不受自动相关性的影响，但是随着具有不规则形状的高分形维数的范围的增加而增加。结论基于规则的ad hoc带宽专门设计用于防止估计的家庭范围碎片，其性能优于h ref 和h lscv ，并给出与连续家庭范围估计值一致的h的最小值。选择ad hoc带宽的协议被证明是一致且可重复的。
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