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Rejoinder to 'Ahmed, M.S. (1998). A note on regression-type estimators using multiple auxiliary information.'
Authors:Rahul Mukerjee,T.J. Rao,&   K. Vijayan
Affiliation:Indian Statistical Institute, Calcutta
Abstract:
In the estimators t 3 , t 4 , t 5 of Mukerjee, Rao & Vijayan (1987), b y x and b y z are partial regression coefficients of y on x and z , respectively, based on the smaller sample. With the above interpretation of b y x and b y z in t 3 , t 4 , t 5 , all the calculations in Mukerjee at al. (1987) are correct. In this connection, we also wish to make it explicit that b x z in t 5 is an ordinary and not a partial regression coefficient. The 'corrected' MSEs of t 3 , t 4 , t 5 , as given in Ahmed (1998 Section 3) are computed assuming that our b y x and b y z are ordinary and not partial regression coefficients. Indeed, we had no intention of giving estimators using the corresponding ordinary regression coefficients which would lead to estimators inferior to those given by Kiregyera (1984). We accept responsibility for any notational confusion created by us and express regret to readers who have been confused by our notation. Finally, in consideration of the above, it may be noted that Tripathi & Ahmed's (1995) estimator t 0 , quoted also in Ahmed (1998), is no better than t 5 of Mukerjee at al. (1987).
Keywords:calculus of factorial arrangements    carry-over effect of order k    cross-over designs    direct effects    interactions    strong balance of order k    universal optimality.
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