Sankhya: The Indian Journal of Statistics

1997, Volume 59, Series A, Pt. 2, 232-241

SOME STRUCTURAL PROPERTIES OF THE BHATTACHARYYA MATRICES

By

ABDULGHANI A.G. ALHARBI, King Abdulaziz University, Madinah

D. N. SHANBHAG, Sheffield University, Sheffield

And

L. THABANE, Western Ontario University, Ontario

SUMMARY. In this paper, we study the structure of the 2X2 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 Bhattacharya matrix.

 

AMS (1991) subject classification. 62E10, 60E05, 62H10.

Key words and phrases. Characterizations, Bhattacharyya bounds, diagonality of Bhattacharyya matrices, Laha-Lukacs theorems, Seth-Shanbhag-Morris theorems, exponential families.

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