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Accounting for Bias and Uncertainty in Nonlinear Stand Density Indices

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Several commonly used stand density indices, such as Reineke's stand density index, Drew and Flewelling's relative density index, and Curtis's relative density index, depend in a nonlinear fashion on stand-level means of measured variables. Thus, the stand-level index value is not necessarily the mean of the plot-level index values. We show formally that this dependency introduces a bias that depends on the sample size or number of plots and on the variance-covariance structure of the measured variables. We then present formulas for estimating the bias and variance or standard error of estimated densities based on a priori knowledge of the variances and covariances or on observed sample data. We also present and compare bootstrap and jackknife methods of estimating the bias and variance associated with sample estimates. The results suggest that for some indices, the bias and variance arising from quick "grab samples" may be large enough to be of practical significance. These results have strong implications for the development and interpretation of stocking guides derived from single plots or from measurement schemes other than those employed in practical applications. For. Sci. 45(3):452-457.
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Keywords: -3/2 law; Density management diagram; bootstrap; jackknife

Document Type: Journal Article

Affiliations: Lecturer, Yale School of Forestry and Environmental Studies, 360 Prospect Street, New Haven, CT 06511--Phone (203) 432-5100

Publication date: 1999-08-01

More about this publication?
  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

    2016 Impact Factor: 1.782 (Rank 17/64 in forestry)

    Average time from submission to first decision: 62.5 days*
    June 1, 2016 to Feb. 28, 2017

    Also published by SAF:
    Journal of Forestry
    Other SAF Publications
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