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，但在森林资源清查中由于考虑到无偏性而应用较少。最近开发了一种设计无偏估计器（Kleinn和Vilčko 2006），使用包含区量化每棵树的选择概率-但在现场确定（高阶Voronoi图）很困难。该估算方法将在本项目中进一步发展，用于限制性k树抽样;即点中心四分之一方法和T平方抽样技术。需要新的方法，高阶Voronoi图不适用。此外，我们希望澄清以下研究问题的无限制和限制的k-树抽样：选择概率可以近似回归到容易测量的树间距离的样本点？如何比较无偏估计的限制/非限制k树抽样固定面积图在精度方面不同的点模式？树木制图可以通过集成的野外计算和测量系统进行优化吗？对真实的数据进行理论分析和模拟研究，并进行现场试验。这些结果对森林调查取样和生态取样同样重要。

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.