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  • Articles  (3)
  • Canadian Science Publishing  (3)
  • Springer
  • 2015-2019  (3)
  • 1920-1924
  • 1905-1909
  • 2015  (3)
  • Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition  (3)
  • 1
    Publication Date: 2015-12-01
    Description: The design bias in the sample mean obtained from sampling the trees nearest to points randomly and uniformly distributed over a forested area can be exactly quantified in terms of the Voronoi polygons (V polygons) surrounding each tree in the forest of interest. For this sampling method, the V polygon for a prospective sample tree is its inclusion zone. The sides of such polygons are perpendicular to a line joining adjacent trees and equidistant from these trees. For any individual tree attribute Y, the design bias in such a sample mean for estimating the population mean of Y will be equal to the covariance between Y and V-polygon area V divided by the mean V-polygon area. The bias as a percent of the population mean of Y is the product of the correlation coefficient between Y and V and the coefficients of variation for Y and V multiplied by 100. This implies that attempts to estimate the means of commonly measured individual tree variables such as DBH, basal area, and crown diameter or the area from sampling trees nearest to randomly located points will likely be positively biased, and the magnitude of that bias will depend on the strength of the linear relationship to the V-polygon area, as well as the variability among the V-polygon areas and the variable of interest. It is not obvious whether increment core data will be positively or negatively biased, because this depends on the characteristics of the forest of interest. The main conclusion of the study is that the bias formula derived for unweighted estimation from sampling the tree nearest to a point indicates that bias in the range of 5%–10% or greater can occur in many forest populations.
    Print ISSN: 0045-5067
    Electronic ISSN: 1208-6037
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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  • 2
    Publication Date: 2015-04-01
    Description: A study of the effects of measurement error was conducted on importance sampling and control variate sampling estimators of tree stem volume in which sample diameters are measured at randomly selected upper-stem heights. It was found that these estimators were unbiased in the presence of additive mean zero and multiplicative mean one measurement error applied to random samples of upper-stem diameter squared. However, biases due to measurement error are present if additive or multiplicative error is applied to upper-stem diameter rather than to upper-stem diameter squared. This is significant, as it appears that most of the previous studies on the magnitude of upper-stem diameter measurement error implicitly assume that the mean error is centered around the diameter rather than about the square of the diameter. Application of typical upper-stem measurement error obtained from previous studies to bias formulae derived here indicates that the bias could be a concern for small trees and with additive measurement error within ranges found in previous studies. Formulae for the variances of importance sampling and control variate sampling are derived, which include the contribution of both measurement error and sampling error. Results from previous studies of Monte Carlo integration estimator sampling error are combined with results from studies of upper-stem measurement error to obtain estimates of the typical magnitude of the contribution of measurement error to total estimator variability. Increases in upper-stem sample size may be warranted due to the impact of measurement error if precise estimates of stem volume at the individual-tree level are desired.
    Print ISSN: 0045-5067
    Electronic ISSN: 1208-6037
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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  • 3
    Publication Date: 2015-04-01
    Description: The effects of measurement error on Monte Carlo (MC) integration estimators of individual-tree volume that sample upper-stem heights at randomly selected cross-sectional areas (termed vertical methods) were studied. These methods included critical height sampling (on an individual-tree basis), vertical importance sampling (VIS), and vertical control variate sampling (VCS). These estimators were unbiased in the presence of two error models: additive measurement error with mean zero and multiplicative measurement error with mean one. Exact mathematical expressions were derived for the variances of VIS and VCS that include additive components for sampling error and measurement error, which together comprise total variance. Previous studies of sampling error for MC integration estimators of tree volume were combined with estimates of upper-stem measurement error obtained from the mensurational literature to compute typical estimates of total standard errors for VIS and VCS. Through examples, it is shown that measurement error can substantially increase the total root mean square error of the volume estimate, especially for small trees.
    Print ISSN: 0045-5067
    Electronic ISSN: 1208-6037
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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