摘要翻译：
我们讨论了一种基于图的空间点模式测试方法。该方法属于数据随机图的范畴，近年来被引入并用于统计模式识别。我们的目标是测试完全的空间随机性，以对抗两个或更多类点之间的分离和关联。为了实现这一目标，我们使用了一种特殊的参数化随机有向图，称为邻近捕获有向图(PCD)，它是基于不同类别的数据点的相对位置。我们使用的统计数据是PCD的相对密度。当比例适当时，PCD的相对密度是一个$u$-统计量。我们利用$u$-统计量的标准中心极限理论导出了相对密度的渐近分布。通过Monte Carlo模拟评价了测试统计量的有限样本性能，并通过Pitman渐近效率评价了测试统计量的渐近性能，从而得到了最优的测试参数。此外，本文讨论的方法也适用于多维数据。
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英文标题：
《A New Family of Random Graphs for Testing Spatial Segregation》
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作者：
E. Ceyhan, C. E. Priebe, D. J. Marchette
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最新提交年份：
2008
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test complete spatial randomness against segregation and association between two or more classes of points. To attain this goal, we use a particular type of parametrized random digraph called proximity catch digraph (PCD) which is based based on relative positions of the data points from various classes. The statistic we employ is the relative density of the PCD. When scaled properly, the relative density of the PCD is a $U$-statistic. We derive the asymptotic distribution of the relative density, using the standard central limit theory of $U$-statistics. The finite sample performance of the test statistic is evaluated by Monte Carlo simulations, and the asymptotic performance is assessed via Pitman's asymptotic efficiency, thereby yielding the optimal parameters for testing. Furthermore, the methodology discussed in this article is also valid for data in multiple dimensions.
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PDF链接：
https://arxiv.org/pdf/802.0615