厦门大学在职研究生招生网
王学钦教授在厦门大学经济学院举行了有条件的相关距离讲座。在职研究生讲座的主要内容如下：
有条件依赖的统计推断在许多领域，包括遗传关联研究和图形模型至关重要。经典的措施侧重于线性条件相关，并不能表征非线性条件的关系，包括非单调的关系。为了克服这种局限性，我们引入了多元随机变量任意尺寸的条件依赖的非参数度量。我们的措施具有必要的和直观的属性作为相关指数。简单地说，它是零几乎肯定，当且仅当两个多元随机变量条件独立给出一个第三随机变量。更重要的是，这一措施的样品版本可以优雅表示为V或U形的过程与随机内核的根，并具有理想的理论特性。根据样品的版本中，我们提出了一个测试条件独立性，这被证明是比一些通过我们的数值模拟新近开发的测试功能更强大。我们的试验的优点是更大时给出的第三随机变量的多元随机变量之间的关系，不能表示在一个随机变量与其它的线性或单调函数。我们还表明，样本的措施是一致的和弱收敛，并检验统计是渐近正常。通过应用我们的测试在真实的数据分析，我们能够识别两种条件相关的基因表达，否则不能透露。因此，我们的测量条件的依赖不仅是一个理想的概念，同时也具有重要的实用价值。
原文：Statistical inference on conditional dependence is essential in many fields including genetic association studies and graphical models. The classic measures focus on linear conditional correlations, and are incapable of characterizing non-linear conditional relationship including non-monotonic relationship. To overcome this limitation, we introduces a nonparametric measure of conditional dependence for multivariate random variables with arbitrary dimensions. Our measure possesses the necessary and intuitive properties as a correlation index. Briefly, it is zero almost surely if and only if two multivariate random variables are conditionally independent given a third random variable. More importantly, the sample version of this measure can be expressed elegantly as the root of a V or U-process with random kernels and has desirable theoretical properties. Based on the sample version, we propose a test for conditional independence, which is proven to be more powerful than some recently developed tests through our numerical simulations. The advantage of our test is even greater when the relationship between the multivariate random variables given the third random variable cannot be expressed in a linear or monotonic function of one random variable versus the other. We also show that the sample measure is consistent and weakly convergent, and the test statistic is asymptotically normal. By applying our test in a real data analysis, we are able to identify two conditionally associated gene expressions, which otherwise cannot be revealed. Thus, our measure of conditional dependence is not only an ideal concept, but also has important practical utility.
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