Likelihood Cross-Validation Versus Least Squares Cross- Validation for Choosing the Smoothing Parameter in Kernel Home-Range Analysis

Fixed kernel density analysis with least squares cross-validation (LSCVh) choice of the smoothing parameter is currently recommended for home-range estimation. However, LSCVh has several drawbacks, including high variability, a tendency to undersmooth data, and multiple local minima in the LSCVh function. An alternative to LSCVh is likelihood cross-validation (CVh). We used computer simulations to compare estimated home ranges using fixed kernel density with CVh and LSCVh to true underlying distributions. Likelihood cross-validation generally performed better than LSCVh, producing estimates with better fit and less variability, and it was especially beneficial at sample sizes ,;50. Because CVh is based on minimizing the Kullback-Leibler distance and LSCVh the integrated squared error, for each of these measures of discrepancy, we discussed their foundation and general use, statistical properties as they relate to home-range analysis, and the biological or practical interpretation of these statistical properties. We found 2 important problems related to computation of kernel home-range estimates, including multiple minima in the LSCVh and CVh functions and discrepancies among estimates from current home-range software. Choosing an appropriate smoothing parameter is critical when using kernel methods to estimate animal home ranges, and our study provides useful guidelines when making this decision. (JOURNAL OF WILDLIFE MANAGEMENT 70(3):641–648; 2006)