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D-optimal designs for covariate models
Aloke Dey,Rahul Mukerjee +1 more
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In this paper, the problem of finding D-optimal or D-efficient designs in the presence of covariates is considered under a completely randomized design set-up with v treatments, k covariates and N experimental units.Abstract:
The problem of finding D-optimal or D-efficient designs in the presence of covariates is considered under a completely randomized design set-up with v treatments, k covariates and N experimental units. In contrast to Lopes Troya [Lopes Troya, J., 1982, Optimal designs for covariates models. Journal of Statistical Planning and Inference, 6, 373–419.], who considered this problem in the equireplicate case, we do not assume that N/v is an integer, and this allows us to study situations where no equireplicate design exists. Even when N/v is an integer, it is seen quite counter-intuitively that there are situations where a non-equireplicate design outperforms the best equireplicate design under the D-criterion.read more
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Optimum covariate designs in partially balanced incomplete block (PBIB) design set-ups
TL;DR: In this article, the authors considered the situation where there is some flexibility for selection in the values of the covariates and proposed a more complex set-up of different partially balanced incomplete block (PBIB) designs, which are popular among practitioners.
Journal ArticleDOI
Design issues related to allocation of experimental units with known covariates into two treatment groups
TL;DR: The present work deals with development of a new allocation algorithm that generates efficient allocation in comparison to random allocation and allocation designs already reported in the literature and demonstrates the efficiency of the proposed algorithm.
Journal ArticleDOI
Optimum covariate designs in split-plot and strip-plot design set-ups
TL;DR: In this article, the problem of finding optimum covariate designs for estimation of covariate parameters in standard split-plot and strip-plot design set-ups with the levels of the whole-plot factor in r randomised blocks is considered.
Journal ArticleDOI
Optimum covariate designs in a binary proper equi-replicate block design set-up
TL;DR: The problem of finding the optimum covariate design (OCD) for the estimation of covariate parameters in a binary proper equi-replicate block (BPEB) design model with covariates, which cover a large class of designs in common use, is considered.
Journal ArticleDOI
D-Optimal Designs for Covariate Parameters in Block Design Set Up
TL;DR: In this article, the problem of finding D-optimal design for the estimation of covariate parameters and the treatment and block contrasts in a block design set up in the presence of non-stochastic controllable covariates was considered.
References
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Book
Orthogonal Arrays: Theory and Applications
TL;DR: The Rao Inequalities for Mixed Orthogonal Arrays., 9.2 The Rao InEqualities for mixed Orthogonic Arrays.- 9.4 Construction X4.- 10.1 Constructions Inspired by Coding Theory.
Book
Fractional Factorial Plans
Aloke Dey,Rahul Mukerjee +1 more
TL;DR: Fractional plans and orthogonal arrays have been extensively studied in the literature, see as discussed by the authors for a survey of some of the most relevant works. But nonexistence of fractional plans has been discussed.
Journal ArticleDOI
D-optimal designs of experiments with non-interacting factors
Rainer Schwabe,Werner Wierich +1 more
TL;DR: In this paper, a general result on the D-optimality of product designs for experiments with non-interacting factors is presented, in particular, D-optimal designs can be constructed as a product of those designs which are D -optimal in the corresponding single-factor models.
Journal ArticleDOI
Konkrete optimale Versuchspläne für ein lineares Modell mit einem qualitativen und zwei quantitativen Einflußfaktoren
TL;DR: In this article, the problem of characterizing exact U- or D-optimal designs for a linear model with one qualitative and two quantitative factors of influence is treated, and necessary conditions for optimal designs are derived if no useful characterizations could be found.