D-optimal chemical balance weighing designs with autoregressive errors
نویسندگان
چکیده
منابع مشابه
Optimal designs for regression models with autoregressive errors
In the one-parameter regression model with AR(1) and AR(2) errors we find explicit expressions and a continuous approximation of the optimal discrete design for the signed least square estimator. The results are used to derive the optimal variance of the best linear estimator in the continuous time model and to construct efficient estimators and corresponding optimal designs for finite samples.
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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.
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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...
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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: Metrika
سال: 2012
ISSN: 0026-1335,1435-926X
DOI: 10.1007/s00184-012-0394-8