Guan Yongtao
Division of Biostatistics, Yale University, New Haven, Connecticut 06520, USA.
Biometrics. 2011 Sep;67(3):926-36. doi: 10.1111/j.1541-0420.2010.01517.x. Epub 2010 Dec 6.
We introduce novel regression extrapolation based methods to correct the often large bias in subsampling variance estimation as well as hypothesis testing for spatial point and marked point processes. For variance estimation, our proposed estimators are linear combinations of the usual subsampling variance estimator based on subblock sizes in a continuous interval. We show that they can achieve better rates in mean squared error than the usual subsampling variance estimator. In particular, for n×n observation windows, the optimal rate of n(-2) can be achieved if the data have a finite dependence range. For hypothesis testing, we apply the proposed regression extrapolation directly to the test statistics based on different subblock sizes, and therefore avoid the need to conduct bias correction for each element in the covariance matrix used to set up the test statistics. We assess the numerical performance of the proposed methods through simulation, and apply them to analyze a tropical forest data set.
我们引入了基于回归外推的新方法，以校正空间点过程和标记点过程在子采样方差估计以及假设检验中经常出现的较大偏差。对于方差估计，我们提出的估计器是基于连续区间内子块大小的常用子采样方差估计器的线性组合。我们表明，它们在均方误差方面可以比常用的子采样方差估计器获得更好的速率。特别是，对于n×n观测窗口，如果数据具有有限的依赖范围，则可以实现n(-2)的最优速率。对于假设检验，我们将提出的回归外推直接应用于基于不同子块大小的检验统计量，因此无需对用于设置检验统计量的协方差矩阵中的每个元素进行偏差校正。我们通过模拟评估了所提出方法的数值性能，并将它们应用于分析一个热带森林数据集。
