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Testing Conditional Independence Via Empirical Likelihood

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Author Info
Liangjun Su (University of California, San Diego)
Halbert White (University of California, San Diego)

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Abstract

Let f(y|x,z) (resp. f(y|x) be the conditional density of Y given (X,Z) (resp. X). We construct a class of `smoothed` empirical likelihood-based tests for the conditional independence hypothesis: Pr[f(Y|X,Z)=f(Y|X)]=1. We show that the test statistics are asymptotically normal under the null hypothesis and derive their asymptotic distributions under a sequence of local alternatives. The tests are shown to possess a weak optimality property in large samples. Simulation results suggest that the tests behave well in finite samples. Applications to some economic and financial time series indicate that our tests reveal some interesting nonlinear causal relations which the traditional linear Granger causality test fails to detect.

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Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number 2003-14.

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Date of creation: 11 Jul 2004
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Handle: RePEc:cdl:ucsdec:2003-14

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Keywords: Conditional Independence b-mixing

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  1. Yoon-Jae Whang, 2004. "Smoothed Empirical Likelihood Methods for Quantile Regression Models," Cowles Foundation Discussion Papers 1453, Cowles Foundation, Yale University. [Downloadable!]
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