Some Structural Properties of the Bhattacharyya Matrices

Some Structural Properties of the Bhattacharyya Matrices

In this paper, we study the structure of the 2 × 2 Bhattacharyya matrix relative to an exponential family and identify, amongst other things, the situations under which this matrix is diagonal or has polynomial nondiagonal elements (or is independent of the parameter). We also identify here the fami...

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Veröffentlicht in:Sankhya. Series A 1997-06, Vol.59 (2), p.232-241
Hauptverfasser: Alharbi, Abdulghani A. G., Shanbhag, D. N., Thabane, L.
Format: Artikel
Sprache:eng
Schlagworte:
Binomials
Fisher information
Generating function
Linear transformations
Mathematical domains
Mathematical functions
Matrices
Polynomials
Random variables
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Zusammenfassung:In this paper, we study the structure of the 2 × 2 Bhattacharyya matrix relative to an exponential family and identify, amongst other things, the situations under which this matrix is diagonal or has polynomial nondiagonal elements (or is independent of the parameter). We also identify here the families for which the (1, 1)-th or (1, 2)-th element of the respective Bhattacharyya matrix is proportional to the corresponding element of a prescribed Bhattacharyya matrix.
ISSN:0581-572X