### Abstract

In this paper, we develop a pairwise distance-based testing procedure for conditional symmetry of a random vector given another random vector and apply it to the cases with given and unknown center that is a parametric regression function, respectively. The resulting tests are moments-based and thus the curse of dimensionality can then be greatly alleviated. The asymptotic properties of the test statistics are investigated. The tests can detect local alternatives distinct from the null at a fastest possible convergence rate in hypothesis testing. To determine critical values, a Monte Carlo-based approximation to the limiting null distributions is suggested. We prove that the approximation works even under local alternative hypotheses. Some simulation studies and a real data example are conducted to examine the performance of the tests.

Original language | English (US) |
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Pages (from-to) | 145-162 |

Number of pages | 18 |

Journal | Computational Statistics and Data Analysis |

Volume | 128 |

DOIs | |

State | Published - Dec 1 2018 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*Computational Statistics and Data Analysis*,

*128*, 145-162. https://doi.org/10.1016/j.csda.2018.06.018

}

*Computational Statistics and Data Analysis*, vol. 128, pp. 145-162. https://doi.org/10.1016/j.csda.2018.06.018

**Pairwise distance-based tests for conditional symmetry.** / Niu, Cuizhen; Guo, Xu; Li, Yong; Zhu, Lixing.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Pairwise distance-based tests for conditional symmetry

AU - Niu, Cuizhen

AU - Guo, Xu

AU - Li, Yong

AU - Zhu, Lixing

PY - 2018/12/1

Y1 - 2018/12/1

N2 - In this paper, we develop a pairwise distance-based testing procedure for conditional symmetry of a random vector given another random vector and apply it to the cases with given and unknown center that is a parametric regression function, respectively. The resulting tests are moments-based and thus the curse of dimensionality can then be greatly alleviated. The asymptotic properties of the test statistics are investigated. The tests can detect local alternatives distinct from the null at a fastest possible convergence rate in hypothesis testing. To determine critical values, a Monte Carlo-based approximation to the limiting null distributions is suggested. We prove that the approximation works even under local alternative hypotheses. Some simulation studies and a real data example are conducted to examine the performance of the tests.

AB - In this paper, we develop a pairwise distance-based testing procedure for conditional symmetry of a random vector given another random vector and apply it to the cases with given and unknown center that is a parametric regression function, respectively. The resulting tests are moments-based and thus the curse of dimensionality can then be greatly alleviated. The asymptotic properties of the test statistics are investigated. The tests can detect local alternatives distinct from the null at a fastest possible convergence rate in hypothesis testing. To determine critical values, a Monte Carlo-based approximation to the limiting null distributions is suggested. We prove that the approximation works even under local alternative hypotheses. Some simulation studies and a real data example are conducted to examine the performance of the tests.

UR - http://www.scopus.com/inward/record.url?scp=85050307630&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85050307630&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2018.06.018

DO - 10.1016/j.csda.2018.06.018

M3 - Article

VL - 128

SP - 145

EP - 162

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

ER -