### Abstract

The density of the multiple correlation coefficient is derived by direct integration when the sample covariance matrix has a linear non-central distribution. Using the density, we deduce the null and non-null distribution of the multiple correlation coefficient when sampling from a mixture of two multivariate normal populations with the same covariance matrix. We also compute actual significance levels of the test of the hypothesis Ho: P1.2.p-0 versus Ha:P1.2…p> 0, given the mixture model.

Original language | English |
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Pages (from-to) | 1443-1457 |

Number of pages | 15 |

Journal | Communications in Statistics - Simulation and Computation |

Volume | 19 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jan 1 1990 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Modelling and Simulation

### Cite this

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**Robustness of the multiple correlation coefficient when sampling from a mixture of two multivariate normal populations.** / Amey, Alphonse K.A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Robustness of the multiple correlation coefficient when sampling from a mixture of two multivariate normal populations

AU - Amey, Alphonse K.A.

PY - 1990/1/1

Y1 - 1990/1/1

N2 - The density of the multiple correlation coefficient is derived by direct integration when the sample covariance matrix has a linear non-central distribution. Using the density, we deduce the null and non-null distribution of the multiple correlation coefficient when sampling from a mixture of two multivariate normal populations with the same covariance matrix. We also compute actual significance levels of the test of the hypothesis Ho: P1.2.p-0 versus Ha:P1.2…p> 0, given the mixture model.

AB - The density of the multiple correlation coefficient is derived by direct integration when the sample covariance matrix has a linear non-central distribution. Using the density, we deduce the null and non-null distribution of the multiple correlation coefficient when sampling from a mixture of two multivariate normal populations with the same covariance matrix. We also compute actual significance levels of the test of the hypothesis Ho: P1.2.p-0 versus Ha:P1.2…p> 0, given the mixture model.

UR - http://www.scopus.com/inward/record.url?scp=0010625451&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010625451&partnerID=8YFLogxK

U2 - 10.1080/03610919008812927

DO - 10.1080/03610919008812927

M3 - Article

AN - SCOPUS:0010625451

VL - 19

SP - 1443

EP - 1457

JO - Communications in Statistics Part B: Simulation and Computation

JF - Communications in Statistics Part B: Simulation and Computation

SN - 0361-0918

IS - 4

ER -