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A simultaneous density-integral system for estimating stem profile and biomass: slash pine and willow oak

Parresol, B.R., Thomas, C.E.
Canadian journal of forest research = 1996 v.26 no.5 pp. 773-781
Quercus phellos, Pinus elliottii, stems, biomass, estimation, specific gravity, equations
In the wood utilization industry, both stem profile and biomass are important quantities. The two have traditionally been estimated separately. The introduction of a density-integral method allows for coincident estimation of stem profile and biomass, based on the calculus of mass theory, and provides an alternative to weight-ratio methodology. In the initial development of the technique, sectional bole weight was predicted from a density integral formed from two equations that were fitted independently using ordinary least squares: (1) a stem-profile, or taper, function and (2) a specific gravity function. A test for contemporaneous correlations using slash pine (Pinus elliottii Engelm. var. elliottii) and willow oak (Quercus phellos L.) data showed highly significant correlations between the density integral and the stem-profile equation as well as the specific gravity equation. However, there was little or no correlation between the stem-profile and specific gravity equations. Because contemporaneous correlations exist between some of the equations, more efficient parameter estimation can be achieved through joint-generalized least squares, better known as seemingly unrelated regressions. However, the improvement in efficiency across parameters varies markedly based on the pattern of contemporaneous correlations. A simultaneous system of three equations was derived for slash pine and willow oak with nonlinear constraints across equations. Parameter estimates from seemingly unrelated regressions estimation had smaller standard errors in all cases than those from ordinary least squares estimation. For slash pine, standard errors were reduced by 11 to 29% and for willow oak, by 5 to 20%.