On exact D-optimal designs with 2 two-level factors and n autocorrelated observations

Abstract

D-optimal design, AR(1) process, Markov process, autocorrelated observations, two-level factor,

D-optimal chemical balance weighing designs with autoregressive errors

“…The D-optimality problem is considered for example in Hadamard (1893), Cohn (1967Cohn ( , 1989, Galil andKiefer (1980), Cheng (1980) or Jacroux et al (1983). For ρ = 0, the problem of the D-optimal design was considered in Li and Yang (2005), Yeh and Lo Huang (2005) and Katulska and Smaga (2010). In these papers, the D-optimality problem was solved in some subclasses of…”

“…Yeh and Lo Huang (2005) considered the exact D-optimal designs with 2 two-level factors and n autocorrelated observations. They proved that the design with the design matrixX…”

“…But as it is described in Banerjee (1975), the design from Yeh and Lo Huang (2005) can be used as the design for finding the weights of three objects. It is easy to calculate that…”

D-optimal and highly D-efficient designs with non-negatively correlated observations

“…Unfortunately, the case where G is not the identity matrix, is less explored. When the errors form an AR(1) process, theoretical and numerical search results about A-and D-optimal designs are given in Angelis et al [1], Bora-Senta and Moyssiadis [3], Katulska and Smaga [20,21], Li and Yang [24], Smaga [29,30] and Yeh and Lo Huang [34]. Katulska and Smaga [22], Masaro and Wong [25] and Smaga [29] present some results on the D-optimal designs, when the errors are equally correlated and they have equal variances (the matrix G is completely symmetric).…”

A note on D-optimal chemical balance weighing designs with autocorrelated observations

“…In the case ρ = 0, it is harder to deal with optimality problems. Some results concerning optimal designs in this case are given for example in Angelis et al (2001); Smaga (2012, 2013); Li and Yang (2005); Smaga (2014) and Yeh and Lo Huang (2005), but many problems are still unsolved. In this paper, we extend the results of Katulska and Smaga (2013), where D-optimality of certain designs was proven under ρ ∈ [0, 1/(n − 2)].…”