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Prediction from an Integrated Regression Equation: A Forestry Application
Author(s) -
Gregoire Timothy G.,
Schabenberger Oliver,
Kong Fanzhi
Publication year - 2000
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2000.00414.x
Subject(s) - tapering , tree (set theory) , statistics , mathematics , mean squared prediction error , volume (thermodynamics) , regression , random forest , regression analysis , econometrics , forestry , computer science , machine learning , geography , mathematical analysis , physics , computer graphics (images) , quantum mechanics
Summary. Models to depict the tapering of a tree bole abound in the literature of forest science, and such models are widely used in forestry practice. One important use is the integration of a taper equation to predict the volume of the tree bole. The statistical properties of volume prediction from an integrated taper equation have been obscure. Based on the statistical characteristics of a taper model for the bole's cross‐sectional area, we derive the first two moments of the volume predictor and the prediction error. Bias from the integration is nil. The importance of a reasonable model of the error structure is demonstrated.