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
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.
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References
Kagam, A. M., Linnik, Y. U. V. and Rao, C. R., Characterization Problems in Mathematical Statistics, John Wiley and Sons, New York, 1973.
Teicher, H., Maximum likelihood characterization of distributions,Ann. Math. Statist.,32 (1961), 1214–1222.
Watson, G. S., Statistics on Spheres, John Wiley and Sons, New York, 1983.
Fan, J. Q., The class of invariant distribution under rotation in the subspace, to be submitted toNortheastern Math. J., 1985.
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Project supported by the Science Fund of the Chinese Academy of Sciences.
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Fan, J., Fang, K. Maximum likelihood character of distributions. Acta Mathematicae Applicatae Sinica 3, 358–363 (1987). https://doi.org/10.1007/BF02008374
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DOI: https://doi.org/10.1007/BF02008374