### Abstract

A random vector originates from one of r known normal populations having a common covariance matrix. We wish to reduce the dimension of the vector by means of a linear map from the original space down to a space of lower dimension while keeping the populations as separate as possible. The commonly used linear maps which are optimal for a class of measures of separation may be very poor in terms of a different criterion: the probability of correct classification calculated with no prior information about the population of origin.

Original language | English (US) |
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Pages (from-to) | 323-330 |

Number of pages | 8 |

Journal | Journal of Statistical Planning and Inference |

Volume | 14 |

Issue number | 2-3 |

DOIs | |

State | Published - 1986 |

Externally published | Yes |

### Fingerprint

### Keywords

- Allocation
- Linear discrimination
- Probability of correct classification
- Separation

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Applied Mathematics
- Statistics and Probability

### Cite this

**Some remarks on allocatory and separatory linear discrimination.** / McCulloch, Robert.

Research output: Contribution to journal › Article

*Journal of Statistical Planning and Inference*, vol. 14, no. 2-3, pp. 323-330. https://doi.org/10.1016/0378-3758(86)90170-9

}

TY - JOUR

T1 - Some remarks on allocatory and separatory linear discrimination

AU - McCulloch, Robert

PY - 1986

Y1 - 1986

N2 - A random vector originates from one of r known normal populations having a common covariance matrix. We wish to reduce the dimension of the vector by means of a linear map from the original space down to a space of lower dimension while keeping the populations as separate as possible. The commonly used linear maps which are optimal for a class of measures of separation may be very poor in terms of a different criterion: the probability of correct classification calculated with no prior information about the population of origin.

AB - A random vector originates from one of r known normal populations having a common covariance matrix. We wish to reduce the dimension of the vector by means of a linear map from the original space down to a space of lower dimension while keeping the populations as separate as possible. The commonly used linear maps which are optimal for a class of measures of separation may be very poor in terms of a different criterion: the probability of correct classification calculated with no prior information about the population of origin.

KW - Allocation

KW - Linear discrimination

KW - Probability of correct classification

KW - Separation

UR - http://www.scopus.com/inward/record.url?scp=46149140258&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=46149140258&partnerID=8YFLogxK

U2 - 10.1016/0378-3758(86)90170-9

DO - 10.1016/0378-3758(86)90170-9

M3 - Article

AN - SCOPUS:46149140258

VL - 14

SP - 323

EP - 330

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 2-3

ER -