Crown profile modeling of loblolly pine by nonparametric regression analysis

Abstract

Crown profile of loblolly pine (Pinus taeda L.) was modeled by nonparametric regression analysis. Nonparametric regression may be applicable when an underlying parametric model cannot be identified and uses only the data to fit a curve. A class of local-polynomial estimators which contains the popular kernel estimator as a special case was investigated. Kernel regression appears to fit closely to the interior data points but often possesses bias problems at the boundaries of the data, a feature less exhibited by local linear or local quadratic regression. A selection of trees was used to show that nonparametric regression captures more variation in crown shape than multiple linear regression. When using nonparametric regression, decisions must be made regarding polynomial order and bandwidth. Such decisions depend on the presence of local curvature, desired degree of smoothing, and for bandwidth in particular, the minimization of some global error criterion. In the present study, a penalized PRESS criterion (PRESS*) was selected as the global error criterion.