Comparison of least-squares cross-validation bandwidth options for kernel home-range estimation

In radiotracking studies, kernel estimation commonly is used to calculate an animal's utilization distribution from location data. A major limitation of kernel-based methods is their high sensitivity to bandwidth values. Least-squares cross-validation (LSCV) is the recommended default bandwidth selection method in ecological literature and is widely available in home-range software. However, various forms of the LSCV method may perform differently in terms of bias and precision. We used simulations to compare the performance of several LSCV forms, including the commonly used scaling approach, as well as sphering, bivariate score function, and univariate alternatives. We combined 2, 4, or 16 bivariate normal distributions and generated sample sizes of 50 or 150 points from each mixture distribution. We calculated absolute bias in home-range size estimates at contours of 99, 95, 75, 50, and 25%. Using the Volume of Intersection (VI) Index, we examined surface fit between each estimated and true distribution. All LSCV forms generally were better than the reference bandwidth. No LSCV option was uniformly best, but the scaling and sphering approaches were slightly better across all contours. Univariate LSCV was similar to other options at outer contours and in surface fit but performed worse at inner contours and was most inconsistent. Using the global versus largest local minimum was unimportant in our comparisons. Although differences among LSCV options were small, these differences could add to variability of kernel estimates across studies. Further evaluation of "second generation" methods (e.g., plug-in approaches) is warranted.