Fixed-count density estimation with virtual plots

It is demonstrated that the expected distance (r)(r) from a random sample location to the kkth nearest tree (rk)(rk) can be predicted with good precision via a proposed generic relationship between rk,rk−1rk,rk−1, and rk−2rk−2. The relationship affords mm-step-ahead predictions which are exploited in a proposed fixed-count (plotless) density estimator. In applications the analyst must first determine the radius (rvirtual)(rvirtual) in a virtual fixed-area circular plot from the observed distances to the kkth nearest point from nn random sample locations. Then the number of point located inside each virtual plot is counted if rk≥rvirtualrk≥rvirtual or predicted via mm-step ahead predictions if rk