Orthogonal Array OA Research Articles

Characterization of triply balanced matrices with applications to survey sampling

R × L triply balanced matrices arise in estimating the mean square errors of nonlinear statistics in survey samplings. It is shown that: (1) Any R × L exact triply balanced matrix and an orthogonal array OA( R, L, 2, 3; λ) are one and the same object up to a possible notational change of the two symbols of the array. (2) R is a multiple of 8 and L ≤ 1 2 R . (3) The problem of the construction of R × L exact triply balanced matrices, 3 ≤ L ≤ 1 2 R , is completely resolved modulo the existence of Hadamard matrices of order 1 2 R . (4) There is no sequence of R × L matrices which are nearly triply balanced in the sense of Rao and Wu (1985) if R < 2 L.