Testing conditional independence via Rosenblatt transforms

Song, Kyungchul

doi:10.1214/09-aos704

Cited by 72 publications

(65 citation statements)

References 30 publications

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“…Linton and Gozalo (2014) develop a non-pivotal nonparametric empirical distribution function based test of conditional independence, the asymptotic null distribution of which is a functional of a Gaussian process. Song (2009) proposes a Rosenblatttransform based test of conditional independence between two random variables given a real function of a random vector. The function is supposed known up to an unknown finite dimensional parameter.…”

Section: Introductionmentioning

confidence: 99%

“…The function is supposed known up to an unknown finite dimensional parameter. Song (2009) suggests to use a wild bootstrap method in a spirit similar to Delgado and González Manteiga (2001) to approximate the distribution function of his test statistics. The latter three tests detect local alternatives to conditional independence that decay to zero at the parametric rate.…”

Section: Introductionmentioning

confidence: 99%

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Nonparametric tests for conditional independence using conditional distributions

Bouezmarni

Taamouti

2014

Journal of Nonparametric Statistics

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. ABSTRACTThe concept of causality is naturally defined in terms of conditional distribution, however almost all the empirical works focus on causality in mean. This paper aims to propose a nonparametric statistic to test the conditional independence and Granger non-causality between two variables conditionally on another one. The test statistic is based on the comparison of conditional distribution functions using an L 2 metric. We use Nadaraya-Watson method to estimate the conditional distribution functions. We establish the asymptotic size and power properties of the test statistic and we motivate the validity of the local bootstrap. We ran a simulation experiment to investigate the finite sample properties of the test and we illustrate its practical relevance by examining the Granger non-causality between S&P 500 Index returns and VIX volatility index. Contrary to the conventional t-test which is based on a linear mean-regression, we find that VIX index predicts excess returns both at short and long horizons.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonparametric tests for conditional independence using conditional distributions

Bouezmarni

Taamouti

2014

Journal of Nonparametric Statistics

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“…Recently, Song (2009) has proposed a distribution-free conditional independence test of two continuous random variables given a parametric single index that achieves the local n 1=2 rate. Speci…cally, Song (2009) tests the hypothesis…”

Section: Introductionmentioning

confidence: 99%

“…A main contribution here is that our proposed test also achieves n 1=2 local power, despite its fully nonparametric nature. In contrast to Song (2009), the conditioning variables can be multi-dimensional; and there are no parameters to estimate. The test is motivated by a series of papers on consistent speci…cation testing by Bierens (1982Bierens ( , 1990), Bierens and Ploberger (1997), and Stinchcombe and White (1998, "StW"), among others.…”

Section: Introductionmentioning

confidence: 99%

A Flexible Nonparametric Test for Conditional Independence

2013

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This paper proposes a nonparametric test for conditional independence that is easy to implement, yet powerful in the sense that it is consistent and achieves n 1=2 local power. The test statistic is based on an estimator of the topological "distance" between restricted and unrestricted probability measures corresponding to conditional independence or its absence. The distance is evaluated using a family of Generically Comprehensively Revealing (GCR) functions, such as the exponential or logistic functions, which are indexed by nuisance parameters. The use of GCR functions makes the test able to detect any deviation from the null. We use a kernel smoothing method when estimating the distance. An integrated conditional moment (ICM) test statistic based on these estimates is obtained by integrating out the nuisance parameters. We simulate the critical values using a conditional simulation approach. Monte Carlo experiments show that the test performs well in …nite samples. As an application, we test the key assumption of unconfoundedness in the context of estimating the returns to schooling.

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“…This is somewhat unexpected, given that nonparametric goodness-of-fit tests that involve random vectors of a multi-dimension and have nontrivial power against n −1/2 -converging Pitman sequences are not often distribution free. Exceptions are tests that use an innovation martingale approach (see, e.g., Khmaladze (1993), Stute, Thies and Zhu (1998), Bai (2003), and Khmaladze and Koul (2004)) or tests for a null hypothesis that has a specific functional form (see, e.g., Blum, Kiefer, and Rosenblatt (1961), Delgado and Mora (2000) and Song (2009)). …”

Section: Introductionmentioning

confidence: 99%

Testing functional inequalities

Lee¹,

Song²,

Whang³

2011

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Abstract. This paper develops tests for inequality constraints of nonparametric regression functions. The test statistics involve a one-sided version of L p -type functionals of kernel estimators. Drawing on the approach of Poissonization, this paper establishes that the tests are asymptotically distribution free, admitting asymptotic normal approximation. Furthermore, the tests have nontrivial local power against a certain class of local alternatives converging to the null at the rate of n −1/2 . Some results from Monte Carlo simulations are presented.

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Testing conditional independence via Rosenblatt transforms

Cited by 72 publications

References 30 publications

Nonparametric tests for conditional independence using conditional distributions

Nonparametric tests for conditional independence using conditional distributions

A Flexible Nonparametric Test for Conditional Independence

Testing functional inequalities

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