An adaptive composite density estimator for k-tree sampling

Steen Magnussen, Pacific Forestry Centre
Lutz Fehrman, Universität Göttingen
William J. Platt, Louisiana State University


Density estimators for k-tree distance sampling are sensitive to the amount of extra Poisson variance in distances to the kth tree. To lessen this sensitivity, we propose an adaptive composite estimator (COM). In simulated sampling from 16 test populations, a three-component composite density estimator (COM)-with weights determined by a multinomial logistic function of four readily available ancillary variables-was identified as superior in terms of average relative absolute bias. Results from a different set of nine validation populations-with widely different stem densities and spatial patterns of tree locations-confirmed that relative root mean squared errors (RRMSE) of COM were, on average, considerably lower than those obtained with the three-component k-tree density estimators. The RRMSE performance of COM improved with increasing values of k. With k = 6 and sample sizes of 10, 20, and 30, the average relative bias of COM was between -5 and 5% in seven validation populations but in an open low-density savanna-like population bias reached -12% (1979 data) and 7% (1996 data). For k = 6 and n = 10, the RRMSE of COM was, in six of the nine validation populations, within 3.3 percentage points of the RRMSE for sampling with fixed-area plots. Jackknife estimates of the precision of COM estimates of density were negatively biased, leading to under-coverage (7%) of computed 95% confidence intervals. © 2011 Springer-Verlag.