# Maximum likelihood character of distributions

Maximum likelihood character of distributions In this paper, some distribution in the family of those with invariance under orthogonal transformations within ans-dimensional linear subspace are characterized by maximun likelihood criteria. Specially, the main result is: supposeP v is a projection matrix of a givens-dimensional subspaceV, andx 1, ...,x n > are i.i.d. samples drawn from population with a pdff(x′P v x), wheref(·) is a positive and continuously differentiable function. ThenP v (M n ) is the maximum likelihood estimator ofP v iff $$f(x) = c_k exp(kx)(k > 0)$$ where $$M_n = \sum\limits_{i = 1}^n {x_i x'_i ,P_u (M_n ) = \sum\limits_{i = 1}^n {\hat \xi _i \hat \xi '_i ,\lambda _1 , \cdot \cdot \cdot ,\lambda _2 } }$$ are the firsts largest eigenvalues of matrixM n , and $$\hat \xi _1 , \cdot \cdot \cdot ,\hat \xi _2$$ , are their associated eigenvectors. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# Maximum likelihood character of distributions

, Volume 3 (4) – Jul 13, 2005
6 pages

/lp/springer-journals/maximum-likelihood-character-of-distributions-Lv7s6mey6Q
Publisher
Springer Journals
Copyright © 1987 by Science Press, Beijing, China and Allerton Press, Inc. New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02008374
Publisher site
See Article on Publisher Site

### Abstract

In this paper, some distribution in the family of those with invariance under orthogonal transformations within ans-dimensional linear subspace are characterized by maximun likelihood criteria. Specially, the main result is: supposeP v is a projection matrix of a givens-dimensional subspaceV, andx 1, ...,x n > are i.i.d. samples drawn from population with a pdff(x′P v x), wheref(·) is a positive and continuously differentiable function. ThenP v (M n ) is the maximum likelihood estimator ofP v iff $$f(x) = c_k exp(kx)(k > 0)$$ where $$M_n = \sum\limits_{i = 1}^n {x_i x'_i ,P_u (M_n ) = \sum\limits_{i = 1}^n {\hat \xi _i \hat \xi '_i ,\lambda _1 , \cdot \cdot \cdot ,\lambda _2 } }$$ are the firsts largest eigenvalues of matrixM n , and $$\hat \xi _1 , \cdot \cdot \cdot ,\hat \xi _2$$ , are their associated eigenvectors.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

### References

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