### Abstract

In this paper, some distribution in the family of those with invariance under orthogonal transformations within an s-dimensional linear subspace are characterized by maximun likelihood criteria. Specially, the main result is: suppose P_{v} is a projection matrix of a given s-dimensional subspace V, and x_{1}, ..., x_{n}> are i.i.d. samples drawn from population with a pdf f(x′P_{v}x), where f(·) is a positive and continuously differentiable function. Then P_{v}(M_{n}) is the maximum likelihood estimator of P_{v} iff {Mathematical expression} where {Mathematical expression} are the first s largest eigenvalues of matrix M_{n}, and {Mathematical expression}, are their associated eigenvectors.

Original language | English (US) |
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Pages (from-to) | 358-363 |

Number of pages | 6 |

Journal | Acta Mathematicae Applicatae Sinica |

Volume | 3 |

Issue number | 4 |

DOIs | |

State | Published - Oct 1 1987 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Applied Mathematics

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## Cite this

*Acta Mathematicae Applicatae Sinica*,

*3*(4), 358-363. https://doi.org/10.1007/BF02008374