A Projection Based Conditional Dependence Measure with Applications to High-dimensional Undirected Graphical Models

Jianqing Fan; Yang Feng; Lucy Xia

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arXiv · 1501.01617

A Projection Based Conditional Dependence Measure with Applications to High-dimensional Undirected Graphical Models

Jianqing Fan·Yang Feng·Lucy Xia

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Abstract

Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding conditional independence test is developed with the asymptotic null distribution unveiled where the number of factors could be high-dimensional. It is also shown that the new test has control over the asymptotic significance level and can be calculated efficiently. A generic method for building dependency graphs without Gaussian assumption using the new test is elaborated. Numerical results and real data analysis show the superiority of the new method.

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Jianqing Fan, Yang Feng, Lucy Xia. 2015-01-07. A Projection Based Conditional Dependence Measure with Applications to High-dimensional Undirected Graphical Models. https://arxiv.org/abs/1501.01617

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