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Journal ArticleDOI

Robustness of Variance Balanced Block Designs

01 Nov 2014-Vol. 76, Iss: 2, pp 305-316
TL;DR: In this article, the robustness of block designs against missing observations is revisited and a lower bound of this criterion for the loss of any t observations in binary variance balanced block design is obtained.
Abstract: The robustness of block designs against missing observations is revisited. It has been shown that A-efficiency criterion is not an appropriate measure to judge the efficiency of the residual design. As an alternate to this, E-efficiency criterion is defined. A lower bound of this criterion for the loss of any t observations in binary variance balanced block design is obtained. Balanced incomplete block designs (BIBD) that are robust as per E-efficiency criterion are identified.
Citations
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Journal ArticleDOI
TL;DR: In most experiments, missing data can hardly be prevented in most experiments due to setbacks that occur during the data entry process, and may grossly affect the estimation of the regression coefficients as mentioned in this paper.
Abstract: Missing data can hardly be prevented in most experiments due to setbacks that occur during the data entry process, and may grossly affect the estimation of the regression coefficients. The effects ...

3 citations

Journal ArticleDOI
01 Feb 2021
TL;DR: This research proposes a sequential experimentation method to separate 2FIs from blocks and assign contributing percentages to each blocked noise factor, and is evaluated and compared to foldover, semifold, and D‐optimal augmentation.

1 citations

Journal ArticleDOI
TL;DR: In this paper, the robustness of binary incomplete block designs against giving rise to a disconnected design in the event of observation loss is investigated, and a link is established between the E-value of a planned design and the extent of observed loss that can be experienced while still guaranteeing an eventual design from which all treatment contrasts can be estimated.
Abstract: This article investigates the robustness of binary incomplete block designs against giving rise to a disconnected design in the event of observation loss. A link is established between the E-value of a planned design and the extent of observation loss that can be experienced while still guaranteeing an eventual design from which all treatment contrasts can be estimated. Patterns of missing observations covered include loss of entire blocks and loss of individual observations. Simple bounds are provided enabling practitioners to easily assess the robustness of a planned design.

1 citations


Cites background from "Robustness of Variance Balanced Blo..."

  • ...Related work is by Srivastava, Gupta, and Dey (1991), Das and Kageyama (1992), Ghosh, Rao, and Singhi (1983), and Bhar (2014)....

    [...]

References
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Journal ArticleDOI
TL;DR: In this paper, the authors show that many commonly employed symmetrical designs such as Balanced Incomplete Block Designs (BIBDs), Latin Squares (LS's), Youden Squares, etc., have optimum properties among the class of non-randomized designs.
Abstract: Many commonly employed symmetrical designs such as Balanced Incomplete Block Designs (BIBD's), Latin Squares (LS's), Youden Squares (YS's), etc., are shown to have optimum properties among the class of non-randomized designs (Section 3). This represents an extension of a property first proved by Wald for LS's in [1]; a similar property demonstrated by Ehrenfeld for LS's in [2] (as well as a third optimum property considered here) is shown to be an immediate consequence of the Wald property, and the Wald property is shown to be the more relevant when one considers optimality rigorously (Section 2). Surprisingly, all of these optimum properties fail to hold if randomized designs are considered (Section 4); the results of Sections 2 and 3, as well as those appearing previously in the literature (as in [1], [2], [3]) must be interpreted in this sense. Generalizations of the BIBD's and YS's, for which analogous results hold, are introduced.

253 citations

Journal ArticleDOI
TL;DR: In this paper, a robustness property of balanced incomplete block designs (BIBDs) with parameters v, b, r, k, k and λ against the unavailability of data in the sense that, when any t, a positive integer, observations are unavailable the design remains connected w.r.t.

49 citations

Journal ArticleDOI
TL;DR: In this paper, Ghosh et al. derived sufficient conditions for the maximal robustness of binary and connected block designs with respect to the estimability of treatment contrasts and variance-and efficiency-balanced block designs.

28 citations

Journal ArticleDOI
TL;DR: In this paper, the robustness of designed experiments for estimating linear functions of a subset of parameters in a general linear model against the loss of any t(U 1) observations is investigated.
Abstract: This paper investigates the robustness of designed experiments for estimating linear functions of a subset of parameters in a general linear model against the loss of any t( U 1) observations. Necessary and sufficient conditions for robustness of a design under a homoscedastic model are derived. It is shown that a design robust under a homoscedastic model is also robust under a general heteroscedastic model with correlated observations. As a particular case, necessary and sufficient conditions are obtained for the robustness of block designs against the loss of data. Simple sufficient conditions are also provided for the binary block designs to be robust against the loss of data. Some classes of designs, robust up to three missing observations, are identified. A-efficiency of the residual design is evaluated for certain block designs for several patterns of two missing observations. The efficiency of the residual design has also been worked out when all the observations in any two blocks, not necessarily ...

19 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigated the robustness of block designs when any observations in a block are lost, in terms of efficiency of the residual design and showed that the covered designs are fairly robust against the unavailability of any number of observations in the block.

19 citations