Optimal Covariate Designs by Premadhis Das Ganesh Dutta Nripes Kumar Mandal & Bikas Kumar Sinha

Author:Premadhis Das, Ganesh Dutta, Nripes Kumar Mandal & Bikas Kumar Sinha
Language: eng
Format: epub
Publisher: Springer India, New Delhi

Similarly we can define another matrix B of order where sub-vector in B stands for of the A -matrix. Actually

This is to be noted that block size and for all . Now we construct the matrix of order as follows:

Let C denote the jth set of v columns of C , , i.e.

(6.4.3)

Using the properties (b) and (c) of the Q-matrix, we can easily check that , where ‘*’ denotes the Hadamard product .

Step 3:

For fixed , let us define the following matrix as

(6.4.4)

We show below that gives an optimum W-matrix for a BPEBD d(v, bt, rt, k).

From the properties of and h it can be proved that(i) 1 W as

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