Maximum likelihood character of distributions

Jianqing Fan, Kaitai Fang

Research output: Contribution to journalArticlepeer-review


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 Pv is a projection matrix of a given s-dimensional subspace V, and x1, ..., xn> are i.i.d. samples drawn from population with a pdf f(x′Pvx), where f(·) is a positive and continuously differentiable function. Then Pv(Mn) is the maximum likelihood estimator of Pv iff {Mathematical expression} where {Mathematical expression} are the first s largest eigenvalues of matrix Mn, and {Mathematical expression}, are their associated eigenvectors.

Original languageEnglish (US)
Pages (from-to)358-363
Number of pages6
JournalActa Mathematicae Applicatae Sinica
Issue number4
StatePublished - Oct 1987
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


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