Volume and Error Variance Estimation Using Integrated Stem Taper Models

Abstract

In this study, we propose two volume and error variance estimators based on an integrated nonlinear mixed-effects stem taper model. The estimators rely either on a first- or a second-order Taylor series expansion. They were first tested through Monte Carlo simulations. The accuracy of the volume and error variance estimates was then tested against more than 1,000 observations. Empirical and nominal coverage of the confidence intervals were also compared under the assumption of a Gaussian distribution. For the volume estimators, results showed that the first-order estimator tends to slightly underestimate the volume, mainly because the stem taper model had random effects specified in a nonlinear manner. The second-order estimator was more accurate with neither under- nor overestimations of volume. For both the first- and the second-order variance estimators, the confidence intervals had empirical coverage that closely matches nominal coverage for probability levels >0.9. Although the proposed estimators require the stem taper model to predict the squared diameter of the cross section, they have the benefit of providing a tractable estimate of the variance. The covariances between different stem sections are quickly estimated because there is no need for repeated numerical integrations.