Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 1 ,pp. 49-56

GOODNESS OF YATES-RAO PROCEDURE FOR RECOVERY OF INTER-BLOCK INFORMATION

By

C.G. BHATTACHARYA, Indian Statistical Institute, New Delhi

SUMMARY.The paper is concerned with the estimation problem for a proper block design with recovery of inter-block information for which numerous procedures are available in the literature with very little known about their relative merits. A desirable property, termed here as goodness, of any such procedure is the natural requirement that it should not, under any circumstances, lead to loss of efficiency compared to the usual procedure without recovery of inter-block information. So far, this has been theoretically investigated only in the case of the Yates-Rao procedure and yielded fragmentary results. The purpose of the present paper is to supercede these results by providing the necessary and sufficient condition for goodness of the Yates-Rao procedure in the case of any proper block design excluding the rare cases where the application of the procedure without truncation of the estimated variance ratio can give rise to a negative weight for the inter-block estimator.

AMS (1991) subject classification. Primary 62F10, 62K10; secondary 62J10.

Key words and phrases. Proper block design, intra-block analysis, inter-block analysis, combined analysis, basic contrasts, combined estimator, linear model, unbiased estimator, ANOVA, BIBD, PBIBD.

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