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

Research output: Contribution to journalArticle

4 Citations (Scopus)

### 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 1443-1457 15 Communications in Statistics - Simulation and Computation 19 4 https://doi.org/10.1080/03610919008812927 Published - Jan 1 1990

### Fingerprint

Multiple Correlation Coefficient
Normal Population
Multivariate Normal
Covariance matrix
Sampling
Robustness
Sample Covariance Matrix
Significance level
Mixture Model
Null
Deduce

### All Science Journal Classification (ASJC) codes

• Statistics and Probability
• Modelling and Simulation

### Cite this

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title = "Robustness of the multiple correlation coefficient when sampling from a mixture of two multivariate normal populations",
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.",
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language = "English",
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journal = "Communications in Statistics Part B: Simulation and Computation",
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In: Communications in Statistics - Simulation and Computation, Vol. 19, No. 4, 01.01.1990, p. 1443-1457.

Research output: Contribution to journalArticle

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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

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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.

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