title: Model errors in tree biomass estimates computed with an approximation to a missing covariance matrix.
abstract: BACKGROUND
  Biomass and carbon estimation has become a priority in national and regional forest inventories. Biomass of individual trees is estimated using biomass equations. A covariance matrix for the parameters in a biomass equation is needed for the computation of an estimate of the model error in a tree level estimate of biomass. Unfortunately, many biomass equations do not provide key statistics for a direct estimation of model errors. This study proposes three new procedures for recovering missing statistics from available estimates of a coefficient of determination and sample size. They are complementary to a recently published study using a computationally intensive Monte Carlo approach.
  
  
  RESULTS
  Our recovery approach use survey data from the population targeted for an estimation of tree biomass. Examples from Germany and Mexico illustrate and validate the methods. Applications with biomass estimation and robust recovered fit statistics gave reasonable estimates of model errors in tree level estimates of biomass.
  
  
  CONCLUSIONS
  It is good practice to provide estimates of uncertainty to any model-dependent estimate of above ground biomass. When a direct approach to estimate uncertainty is impossible due to missing model statistics, the proposed robust procedure is a first step to good practice. Our recommended approach offers protection against inflated estimates of precision.
authors.affiliation: Natural Resources Canada, 506 West Burnside Road, Victoria, BC V8Z 1M5 Canada.
authors.forename: Steen
authors.initials: S
authors.lastname: Magnussen
authors.affiliation: CONAFOR, Periférico Poniente #5360 Col. San Juan de Ocotán, C.P. 45019 Zapopan, Jalisco Mexico.
authors.forename: Oswaldo Ismael
authors.initials: OI
authors.lastname: Carillo Negrete
keywords: Linear regression; Nonlinear regression; Parametric bootstrap; Residual variance; Robust estimation; Weighted regression