Optimum designs for estimation of regression parameters in a balanced treatment incomplete block design set-up |
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Authors: | Ganesh Dutta Premadhis Das |
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Affiliation: | 1. Indian Statistical Institute, North-East Centre, Tezpur, Assam 784028, India;2. Department of Statistics, University of Kalyani, Kalyani 741235, India |
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Abstract: | The use of covariates in block designs is necessary when the experimental errors cannot be controlled using only the qualitative factors. The choice of values of the covariates for a given set-up attaining minimum variance for estimation of the regression parameters has attracted attention in recent times. In this paper, optimum covariate designs (OCD) have been considered for the set-up of the balanced treatment incomplete block (BTIB) designs, which form an important class of test-control designs. It is seen that the OCDs depend much on the methods of construction of the basic BTIB designs. The series of BTIB designs considered in this paper are mainly those as described by Bechhofer and Tamhane (1981) and Das et al. (2005). Different combinatorial arrangements and tools such as Hadamard matrices and different kinds of products of matrices viz Khatri-Rao product and Kronecker product have been conveniently used to construct OCDs with as many covariates as possible. |
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Keywords: | BTIB design Covariate models Hadamard matrix Khatri-Rao product Kronecker product |
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