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

Abstract 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.