共查询到20条相似文献,搜索用时 15 毫秒
1.
Optimal block designs for a certain type of triallel cross experiments are investigated. Nested balanced block designs are introduced and it is shown how these designs give rise to optimal designs for triallel crosses. Several .series of nested balanced block designs, leading to optimal designs for triallel crosses are reported. 相似文献
2.
John Stufken 《统计学通讯:理论与方法》2013,42(11):3857-3863
We present a class of counerexamples for a conjecture on the existence or linear trend free block designs we will also prove a considerably weakened version of this conjecture which will determine all combinations of designs parmetres for which the class of linear trend free block designs is non empty. 相似文献
3.
John Stufken 《统计学通讯:理论与方法》2013,42(12):3849-3862
A sufficient condition for the Bayes A-optimality of block designs when comparing a standard treatment with v test treatments is given by Majumdar. (In:Optimal Design and Analysis of Experiments, Y. Dodge, V. V. Fedorov and H. P. Wynn (Eds.), 15-27, North-Holland, 1988). The priors that he considers depend on a constant α ε [0, ∞), with α - 0 corresponding to no prior information at all. The given sufficient condition, consequently, also depends on a. Large families of optimal and highly efficient designs are only known for the case α - 0. We will show how some of the results for α - 0 can be extended to obtain large families of optimal and highly efficient designs for arbitrary values of α. In addition, these results are useful when considering design robustness against an improper choice of α. 相似文献
4.
Method of minimum norm quadratic unbiased estimation (MINQUE) is applied to incomplete block designs. Simple formulae are derived for a class of designs which includes the balanced designs. 相似文献
5.
Ravindra Khattree 《统计学通讯:理论与方法》2013,42(20):5165-5168
AbstractDue to important practical applications and considerations in biomedical clinical trials, fixed block-sum designs are of interest. We show that in general, the constant block-sum balanced incomplete block designs do not exist. 相似文献
6.
Dexter C. Whittinghill III 《统计学通讯:理论与方法》2013,42(1):277-285
Trend-free and nearly trend-free block designs were developed to eliminate polynomial trends across the plots of experimental designs. Yeh, Bradley and Notz (1985) proved that certain nearly trend-free designs are A- and D-optimal in a subclass of all competing designs. This article extends that result by enlarging the class of designs for which the optimality holds, and by increasing the class of optimality criteria from A- and D-optimality to the class of all Schur-convex nonincreasing functions. 相似文献
7.
In the present paper an attempt has been made to characterize and unify the three different concepts of balancing in incomplete block designs, namely (i) variance balance, (ii) efficiency balance and (iii) pairwise balance. Simple characterizations of variance balance and efficiency balance have been given using the P matrix. A method of constructing efficiency balanced (EB) and variance balanced designs has also been presented. 相似文献
8.
9.
In this paper a method of constructing group-divisible incomplete block designs has been suggested. A series of balanced incomplete block designs has also been obtained. 相似文献
10.
Parneet Kaur 《统计学通讯:理论与方法》2020,49(6):1462-1474
AbstractThe present article deals with the study of association among the elements of a Sudoku square. In this direction, we have defined an association scheme and constructed incomplete Sudoku square designs which are capable of studying four explanatory variables and also happen to be the designs for two-way elimination of heterogeneity. Some series of Partially Balanced Incomplete Block (PBIB) designs have also been obtained. 相似文献
11.
Some methods of construction of generalized binary proper efficiency-balanced block (GB-EB) designs with two different replications are derived and the solution of the unknown designs given by Das and Kageyama (1991) are obtained. 相似文献
12.
Several authors have investigated conditions for a binary block design, D, to be maximally robust such that every eventual design obtained from D by eliminating r[υ]−1 blocks is connected, where r[υ] is the smallest treatment replication. Four new results for the maximal robustness of D with superior properties are given. An extension of these results to widen the assessment of robustness of the planned design is also presented. 相似文献
13.
The theory and properties of trend-free (TF) and nearly trend-free (NTF) block designs are wel1 developed. Applications have been hampered because a methodology for design construction has not been available. This article begins with a short review of concepts and properties of TF and NTF block designs. The major contribution is provision of an algorithm for the construction of linear and nearly linear TF block designs. The algorithm is incorporated in a computer program in FORTRAN 77 provided in an appendix for the IBM PC or compatible microcomputer, a program adaptable also to other computers. Three sets of block designs generated by the program are given as examples. A numerical example of analysis of a linear trend-free balanced incomplete block design is provided. 相似文献
14.
We provide constructions of cyclic 2-class PBIBD's using cyclotomy in finite fields. Our results give theoretical explanations of the two sporadic examples given by Agrawal (1987). 相似文献
15.
Mike Jacroux 《Journal of statistical planning and inference》1984,9(2):259-267
In this paper we consider proper block designs and derive an upper bound for the number of blocks which can have a fixed number of symbols common with a given block of the design. To arrive at the desired bound, a generalization of an integer programming theorem due to Bush (1976) is first obtained. The integer programming theorem is then used to derive the main result of this paper. The bound given here is then compared with a similar bound obtained by Kageyama and Tsuji (1977). 相似文献
16.
Jennifer Seberry 《Journal of statistical planning and inference》1984,10(1):69-82
Some recursive constructions are given for Bhaskar Rao designs. Using examples of these designs found by Shyam J. Singh, Rakesh Vyas and new ones given here we show the necessary conditions λ≡0 (mod 2), λυ(υ?1)≡0 (mod 24) are sufficient for the existence of Bhaskar Rao designs with one association class and block size 3. This result is used with a result of Street and Rodger to obtain regular partially balanced block designs with 2υ treatments, block size 3, λ1=0, group size 2 and υ groups. 相似文献
17.
Let D be a saturated fractional factorial design of the general K1 x K2 ...x Kt factorial such that it consists of m distinct treatment combinations and it is capable of providing an unbiased estimator of a subvector of m factorial parameters under the assumption that the remaining k-m,t (k = H it ) factorial parameters are negligible. Such a design will not provide an unbiased estimator of the varianceσ2 Suppose that D is an optimal design with respect to some optimality criterion (e.g. d-optimality, a-optimality or e-optimality) and it is desirable to augment D with c treatmentcombinations with the aim to estimate 2 Suppose that D is an optimal design with respect to some optimality criterion (e.g. d-optimality, a-optimality or e-optimality) and it is desirable to augment D with c treatment combinations with the aim to estimate σ2 unbiasedly. The problem then is how to select the c treatment combinations such that the augmented design D retains its optimality property. This problem, in all its generality is extremely complex. The objective of this paper is to provide some insight in the problem by providing a partial answer in the case of the 2tfactorial, using the d-optimality criterion. 相似文献
18.
L. L. Sia 《Revue canadienne de statistique》1977,5(2):227-234
The concept of optimum spacing of an arbitrary group of treatments was introduced by Sinha and Sinha (1969) in a study of the relative efficiencies of a group of block designs. In this paper, the optimum spacings of elementary treatment contrasts in a 2-factor symmetrical block design with Property A are studied using the A-optimality criterion. Conditions for optimum spacings are expressed in terms of the relative magnitudes of the efficiency factors. 相似文献
19.
Incomplete block designs estimating the relative potency free from block effects have been discussed. A method of constructing a series of such designs has been presented. 相似文献
20.
Nripes Kumar Mandal 《统计学通讯:理论与方法》2017,46(5):2364-2369
Orthogonality is an important concept in block design. Necessary and sufficient condition for a connected block design to be orthogonal is well known. However, when a design is not orthogonal, it is not clear how much it deviates from orthogonality. In this paper, an attempt has been made to first define the measures of or indices to non orthogonality in block design and then to characterize designs possessing minimum non orthogonality indices. It is shown that a Balanced Incomplete Block Design (BIBD) and a Balanced Block Design (BBD), if exist, possess this property. 相似文献