### Abstract

In classical statistics the likelihood ratio statistic used in testing hypotheses about covariance matrices does not have a closed form distribution, but asymptotically under strong normality assumptions is a function of the χ2-distribution. This distributional approximation totally fails if the normality assumption is not completely met. In this paper we will present multivariate robust testing procedures for the scatter matrix Σ using S-estimates. We modify the classical likelihood ratio test (LRT) into a robust LRT by substituting the robust estimates in the formula in place of classical estimates. A nonlinear formula is also suggested to approximate the degrees of freedom for the approximated Wishart distribution proposed for S-estimates of the shape matrix Σ. We present simulation results to compare the validity and the efficiency of the robust likelihood test to the classical likelihood test.

Original language | English (US) |
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Pages (from-to) | 863-874 |

Number of pages | 12 |

Journal | Computational Statistics and Data Analysis |

Volume | 49 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1 2005 |

### Keywords

- Likelihood ratio test
- S-estimate

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Statistics, Probability and Uncertainty
- Electrical and Electronic Engineering
- Computational Mathematics
- Numerical Analysis
- Statistics and Probability