### Abstract

This paper explores empirically the first two moments of ratio of the partial sum of the first two sample eigenvalues to the sum of all eigenvalues when the population eigenvalues of a covariance matrix are all the same. Estimation of the first two moments can be practically crucial in assessing non-randomness of observed patterns on planar graphical displays based on lower rank approximations of data matrices. For derivation of the moments, exact and large sample asymptotic distributions of the sample ratios are reviewed but neither can be applicable to derivation of the moments. Therefore, I rely on simulations, where data matrices X with order nxm element-wise independent normal distribution with mean 0 and variance σ^{2} are assumed, that is, X ∼ N(0, σ^{2}I_{nm}), and then derive formulas for estimates of means and standard deviations of the sample ratios within a range of order of the data matrix. The derivations are based on the biplot graphical diagnostic methods proposed by Bradu and Gabriel (1976).

Original language | English (US) |
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Pages (from-to) | 420-427 |

Number of pages | 8 |

Journal | Journal of Modern Applied Statistical Methods |

Volume | 1 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2002 |

### Keywords

- Bias
- Biplot
- Eigenvalues
- Multivariate Gaussian; Schönemann-Lingoes- Gower coefficient

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty