Development of design unbiased estimators for the restricted k-tree sampling techniques PCM (point-centered quarter method) and T-square sampling

K-树抽样在生态抽样中应用较多，而在森林资源清查中应用较少，主要是考虑无偏性。最近开发了一种设计无偏估计器(Kleinn和VilčKo，2006年)，使用了量化每棵树选择概率的包含区--但在现场确定这一点很费力(高阶Voronoi图)。这种估计方法将在本项目中进一步发展，用于限制性k树抽样；即点中心四分之一法和T平方抽样技术。需要新的方法，高阶Voronoi图不适用。此外，我们还希望澄清以下关于非受限和受限k-树抽样的研究问题：是否可以通过将它们回归到采样点处容易测量的树间距离来近似选择概率？对于不同点模式，受限/非受限k-树抽样的无偏估计器与固定面积图的精度如何比较？树木映射能否通过集成的野外计算和测量系统来优化？我们将对真实数据进行理论分析和模拟研究，并进行现场测试。结果对于森林调查抽样和生态抽样同样重要。

k-tree sampling is frequently applied in ecological sampling; less so in forest inventory for the concern of unbiasedness. A design-unbiased estimator had recently been developed (Kleinn and Vilčko 2006), using inclusion zones that quantify the per-tree selection probability - but that are laborious to determine in the field (higher order Voronoi diagrams). That estimation approach shall be further developed in this project for restricted k-tree sampling; that is to the point-centered-quarter method and to the T-square sampling technique. New approaches are required, the higher order Voronoi diagrams do not apply. Also, we wish to clarify the following research questions for both unrestricted and restricted k-tree sampling:Can the selection probability be approximated by regressing them to easily measurable inter-tree distances at the sample point?How compares the unbiased estimator for restricted/unrestricted k-tree sampling to fixed area plots in terms of precision for different point patterns?Can tree mapping be optimized by an integrated field computing and measurement system?Theoretical analyses and simulation studies on real data will be carried and also field testing. The results will be equally important for forest inventory sampling and for ecological sampling.