### 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) |
---|---|

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 |

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### 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

### Cite this

**A robust testing procedure for the equality of covariance matrices.** / Aslam, Shagufta; Rocke, David M.

Research output: Contribution to journal › Article

*Computational Statistics and Data Analysis*, vol. 49, no. 3, pp. 863-874. https://doi.org/10.1016/j.csda.2004.06.009

}

TY - JOUR

T1 - A robust testing procedure for the equality of covariance matrices

AU - Aslam, Shagufta

AU - Rocke, David M

PY - 2005/6/1

Y1 - 2005/6/1

N2 - 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.

AB - 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.

KW - Likelihood ratio test

KW - S-estimate

UR - http://www.scopus.com/inward/record.url?scp=18744375160&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18744375160&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2004.06.009

DO - 10.1016/j.csda.2004.06.009

M3 - Article

AN - SCOPUS:18744375160

VL - 49

SP - 863

EP - 874

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

IS - 3

ER -