منابع مشابه
D-optimal weighing designs for four and five objects
For j = 4 and j = 5 and all d j, the maximum value of detXX , where X runs through all j d (0,1)-matrices, is determined along with a matrix X0 for which the maximum determinant is attained. In the theory of statistical designs, X0 is called a D-optimal design matrix. Design matrices that were previously thought to be D-optimal, are shown here to be D-optimal.
متن کاملTrace-minimal graphs and D-optimal weighing designs
Let G(v, δ) be the set of all δ-regular graphs on v vertices. Certain graphs from among those in G(v, δ) with maximum girth have a special property called trace-minimality. In particular, all strongly regular graphs with no triangles and some cages are trace-minimal. These graphs play an important role in the statistical theory of D-optimal weighing designs. Each weighing design can be associat...
متن کاملNew orthogonal designs from weighing matrices
In this paper we show the existence of new orthogonal designs, based on a number of new weighing matrices of order 2n and weights 2n − 5 and 2n−9 constructed from two circulants. These new weighing matrices were constructed recently by establishing various patterns on the locations of the zeros in a potential solution, in conjunction with the power spectral density criterion. We also demonstrat...
متن کاملWeighing Designs and Methods of Construction
Abstract: It is difficult to weigh the light objects by weighing balance accurately when measured individually. If several light objects are weighed in groups rather than individually then the precision of the estimates increases quite considerably. There are two types of balances one is chemical balance and other is spring balance. Spring balance is similar when only one pan of chemical balanc...
متن کاملD - optimal weighing designs for n ≡ − 1 ( mod 4 ) objects and a large number of weighings
Let Mm,n(0, 1) denote the set of all m× n (0,1)-matrices and let G(m,n) = max{detXX : X ∈Mm,n(0, 1)}. In this paper we exhibit some new formulas for G(m,n) where n ≡ −1 (mod 4). Specifically, for m = nt+r where 0 ≤ r < n, we show that for all sufficiently large t, G(nt+r, n) is a polynomial in t of degree n that depends on the characteristic polynomial of the adjacency matrix of a certain regul...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 1980
ISSN: 0090-5364
DOI: 10.1214/aos/1176345202