标记空间点模式的偏差检验构造和功效比较
Deviation test construction and power comparison for marked spatial point patterns
摘要：
偏差检验属于点过程统计中的核心工具，其中假设通常在原假设下考虑经验汇总函数与其期望值之间的差异进行检验，其取决于距离变量r。这个测试是一个经典的设备，以克服多重比较的问题，出现，因为功能的差异，必须同时考虑一系列的距离r。该测试有三个基本成分：（i）选择合适的汇总函数，（ii）汇总函数的转换或差异的缩放，以及（iii）计算全局偏差度量。我们详细考虑建设这样的测试都平稳和有限的点过程，并显示由两个玩具的例子和模拟研究的情况下的随机标签假设的点（i）和（ii）有很大的影响力的测试。
英文摘要：
The deviation test belong to core tools in point process statistics, where hypotheses are typically tested considering differences between an empirical summary function and its expectation under the null hypothesis, which depend on a distance variable r. This test is a classical device to overcome the multiple comparison problem which appears since the functional differences have to be considered for a range of distances r simultaneously. The test has three basic ingredients: (i) choice of a suitable summary function, (ii) transformation of the summary function or scaling of the differences, and (iii) calculation of a global deviation measure. We consider in detail the construction of such tests both for stationary and finite point processes and show by two toy examples and a simulation study for the case of the random labelling hypothesis that the points (i) and (ii) have great influence on the power of the tests.
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