### Abstract

Three simple and explicit procedures for testing the independence of two multi-dimensional random variables are described. Two of the associated test statistics (L _{1}, log-likelihood) are defined when the empirical distribution of the variables is restricted to finite partitions. A third test statistic is defined as a kernel-based independence measure. All tests reject the null hypothesis of independence if the test statistics become large. The large deviation and limit distribution properties of all three test statistics are given. Following from these results, distribution-free strong consistent tests of independence are derived, as are asymptotically α-level tests. The performance of the tests is evaluated experimentally on benchmark data.

Original language | English |
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Pages (from-to) | 183-198 |

Number of pages | 16 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 5254 LNAI |

DOIs | |

Publication status | Published - Dec 1 2008 |

Event | 19th International Conference on Algorithmic Learning Theory, ALT 2008 - Budapest, Hungary Duration: Oct 13 2008 → Oct 16 2008 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint Dive into the research topics of 'Nonparametric independence tests: Space partitioning and Kernel approaches'. Together they form a unique fingerprint.

## Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*,

*5254 LNAI*, 183-198. https://doi.org/10.1007/978-3-540-87987-9_18