Evaluation of Root-n Bandwidth Selectors for Kernel Density Estimation

The kernel density estimator is used commonly for estimating animal utilization distributions from location data. This technique requires estimation of a bandwidth, for which ecologists often use least-squares cross-validation (LSCV). However, LSCV has large variance and a tendency to under-smooth data, and it fails to generate a bandwidth estimate in some situations. We compared performance of 2 new bandwidth estimators (root-n) versus that of LSCV using simulated data and location data from sharp-shinned hawks (Accipter striatus) and red wolves (Canis rufus). With simulated data containing no repeat locations, LSCV often produced a better fit between estimated and true utilization distributions than did root-n estimators on a case-by-case basis. On average, LSCV also provided lower positive relative error in home-range areas with small sample sizes of simulated data. However, root-n estimators tended to produce a better fit than LSCV on average because of extremely poor estimates generated on occasion by LSCV. Furthermore, the relative performance of LSCV decreased substantially as the number of repeat locations in the data increased. Root-n estimators also generally provided a better fit between utilization distributions generated from subsamples of hawk data and the local densities of locations from the full data sets. Least-squares cross-validation generated more unrealistically disjointed estimates of home ranges using real location data from red wolf packs. Most importantly, LSCV failed to generate home-range estimates for .20% of red wolf packs due to presence of repeat locations. We conclude that root-n estimators are superior to LSCV for larger data sets with repeat locations or other extreme clumping of data. In contrast, LSCV may be superior where the primary interest is in generating animal home ranges (rather than the utilization distribution) and data sets are small with limited clumping of locations.