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1.
This paper deals with the problem of estimating the individual weights of objects with minimum variances by using a weighing
design with non-homogeneity of the variances of errors in the model. The necessary and sufficient conditions for optimum biased
spring balance weighing designs with non-homogeneity of the variances of errors and for optimum chemical balance weighing
designs with non-homogeneity of the variances of errors are given and the relations between these designs are investigated.
New optimum weighing designs are also found.
Department of Mathematical and Statistical Methods, Agricultural University, 60-637 Poznan, Poland; Institute of Mathematics,
Adam Mickiewicz University, 60-769 Poznan, Poland. Published in Lietuvos Matematikos Rinkinys, Vol. 34, No. 3, pp. 267–273,
July–September, 1994. 相似文献
2.
Necessary and sufficient conditions determining D-optimality of chemical balance weighing design with three objects are proved under first-order autoregressive errors with negative autocorrelation. D-optimality of the design constructed by Li and Yang (2005) is also shown. 相似文献
3.
The notion of unbiased orthogonal designs is introduced as a generalization of unbiased Hadamard matrices, unbiased weighing matrices and quasi-unbiased weighing matrices. We provide upper bounds and several methods of construction for mutually unbiased orthogonal designs. As an application, mutually quasi-unbiased weighing matrices for various parameters are obtained. 相似文献
4.
Algebraic techniques are employed to obtain necessary conditions for the existence of certain families of circulant weighing designs. As an application we rule out the existence of many circulant weighing designs. In particular, we show that there does not exist a circulant weighing matrix of order 43 for any weight. We also prove two conjectures of Yosef Strassler. © 1996 John Wiley & Sons, Inc. 相似文献
5.
Construction of nested balanced incomplete block (BIB) designs, nested balanced ternary designs and rectangular designs from given nested BIB designs and resolvable BIB designs are described. New constructions ofq-ary codes from nested BIB designs and balanced bipartite weighing designs are also given. 相似文献
6.
Summary Methods of construction of balancedn-ary designs using difference sets have been studied in this paper. Some properties of balancedn-ary designs are studied. Use of balanced ternary designs has been made to construct some efficient weighing designs.
Institute of Agricultural Research Statistics 相似文献
7.
Summary The purpose of this paper is three-fold. The first purpose is to compile and to systematize published and dispersed results
on two aspects of balancing in incomplete block designs, i.e., pairwise balance and variance balance. This was done in order
to establish the status of these two concepts of balance in published literature and to put them in a form which is useful
for further work in this area. Also, the results in this form are necessary for the development of the remainder of the paper.
The second purpose of this paper is to present a method of constructing unequal replicate and/or unequal block size experiment
designs for which the variance balance property is achieved. The method of construction involves the union of blocks from
two or more block designs and the augmentation of some of the blocks with additional treatments; the method is denoted asunionizing block designs. A straight-forward extension of the method would produce a partially balanced block design with unequal replicate and/or
unequal block designs. The enlargement of the concept and availability of variance blanced block designs to accommodate unequal
replication and/or unequal block sizes is important to the researcher, the teacher, and the experimenter needing such designs.
For example, an animal nutritionist or a psychologist is no longer required to have constant litter or family sizes for the
blocks and may have unequal replication on the treatments for those treatments with insufficient material and still attain
the goal of equal variances on all normalized treatment contracts.
The third purpose of the paper is to apply the unionizing block designs method to construct a family of unequal replicate
and unequal block size variance balanced designs. Some comments are given on the extension of the unionizing block designs
method to construct other families of variance balanced or partially balanced block designs.
This investigation was supported in part by PHS Research Grant No. R01-GM-05900 from General Medical Services. 相似文献
8.
A. Dey 《Annals of the Institute of Statistical Mathematics》1969,21(1):343-346
Summary Banerjee [1], [2] has shown that the arrangements afforded by a Balanced Incomplete Block Design can be used as an efficient
spring balance design. Such designs suffer from one drawback viz., there are only a few or no degrees of freedom left for
the estimation of error-variance,σ
2. To overcome this difficulty, it has been suggested that the whole design may be repeated a certain number of times to get
an estimate of the error variance. In the present note an attempt has been made to give an alternative design where there
is no necessity of such repetition. It has been also shown that these designs give a lesser variance of the estimated weights
than the repeated design.
Institute of Agricultural Research Statistics 相似文献
9.
K. S. Banerjee 《Annals of the Institute of Statistical Mathematics》1974,26(1):447-454
Summary Dey [3] has suggested a spring balance weighing design in preference to “repeated designs”, and later, Kulshreshtha and Dey
[5] have suggested yet one more weighing design which, they say, would be preferred to “repeated designs” and to those suggested
in [3], provided one is interested in estimating the weights of some of the objects with increased precision at the cost of
precision for others. It has been shown here that, while the above findings may be true in some situations, one might, in
a given problem, prefer “repeated designs” to those suggested in [3] and [5].
NSF Grant No. GP-28312 and GP-36562. 相似文献
10.
It is often important to incorporate covariate information in the design of clinical trials. In literature there are many designs of using stratification and covariate-adaptive randomization to balance certain known covariate. Recently, some covariate-adjusted response-adaptive (CARA) designs have been proposed and their asymptotic properties have been studied (Ann. Statist. 2007). However, these CARA designs usually have high variabilities. In this paper, a new family of covariate-adjusted response-adaptive (CARA) designs is presented. It is shown that the new designs have less variables and therefore are more efficient. 相似文献
11.
Joe Masaro 《Linear algebra and its applications》2008,429(7):1392-1408
Suppose that Y=(Yi) is a normal random vector with mean Xb and covariance σ2In, where b is a p-dimensional vector (bj),X=(Xij) is an n×p matrix. A-optimal designs X are chosen from the traditional set D of A-optimal designs for ρ=0 such that X is still A-optimal in D when the components Yi are dependent, i.e., for i≠i′, the covariance of Yi,Yi′ is ρ with ρ≠0. Such designs depend on the sign of ρ. The general results are applied to X=(Xij), where Xij∈{-1,1}; this corresponds to a factorial design with -1,1 representing low level or high level respectively, or corresponds to a weighing design with -1,1 representing an object j with weight bj being weighed on the left and right of a chemical balance respectively. 相似文献
12.
Bronislaw Ceranka Malgorzata Graczyk 《Journal of Applied Mathematics and Computing》2004,16(1-2):143-150
In this paper we study the estimation problem of individual weights of objects using an A-optimal chemical balance weighing design. We assume that in this model errors are correlated and they have the same variances. The lower bound oftr (X′G ?1 X)?1 is obtained and a necessary and sufficient condition for this lower bound to be attained is given. There is given new construction method of A-optimal chemical balance weighing design. 相似文献
13.
Minimum secondary aberration fractional factorial split-plot designs in terms of consulting designs 总被引:1,自引:0,他引:1
AI Mingyao & ZHANG Runchu Key Laboratory of Pure Applied Mathematics School of Mathematical Sciences Peking University Beijing China Key Laboratory of Pure Mathematics Combinatorics School of Mathematical Sciences Nankai University Tianjin China 《中国科学A辑(英文版)》2006,49(4):494-512
It is very powerful for constructing nearly saturated factorial designs to characterize fractional factorial (FF) designs through their consulting designs when the consulting designs are small. Mukerjee and Fang employed the projective geometry theory to find the secondary wordlength pattern of a regular symmetrical fractional factorial split-plot (FFSP) design in terms of its complementary subset, but not in a unified form. In this paper, based on the connection between factorial design theory and coding theory, we obtain some general and unified combinatorial identities that relate the secondary wordlength pattern of a regular symmetrical or mixed-level FFSP design to that of its consulting design. According to these identities, we further establish some general and unified rules for identifying minimum secondary aberration, symmetrical or mixed-level, FFSP designs through their consulting designs. 相似文献
14.
Orthogonal designs are a natural generalization of the Baumert-Hall arrays which have been used to construct Hadamard matrices. We continue our investigation of these designs and show that orthogonal designs of type (1,k) and ordern exist for everyk < n whenn = 2 t+2?3 andn = 2 t+2?5 (wheret is a positive integer). We also find orthogonal designs that exist in every order 2n and others that exist in every order 4n. Coupled with some results of earlier work, this means that theweighing matrix conjecture ‘For every ordern ≡ 0 (mod 4) there is, for eachk ?n, a square {0, 1, ? 1} matrixW = W(n, k) satisfyingWW t =kIn’ is resolved in the affirmative for all ordersn = 2t+1?3,n = 2t+1?5 (t a positive integer). The fact that the matrices we find are skew-symmetric for allk < n whenn ≡ 0 (mod 8) and because of other considerations we pose three other conjectures about weighing matrices having additional structure and resolve these conjectures affirmatively in a few cases. In an appendix we give a table of the known results for orders ? 64. 相似文献
15.
Yury J. Ionin 《Discrete Mathematics》2006,306(14):1557-1568
The first infinite families of symmetric designs were obtained from finite projective geometries, Hadamard matrices, and difference sets. In this paper we describe two general methods of constructing symmetric designs that give rise to the parameters of all other known infinite families of symmetric designs. The method of global decomposition produces an incidence matrix of a symmetric design as a block matrix with each block being a zero matrix or an incidence matrix of a smaller symmetric design. The method of local decomposition represents incidence matrices of a residual and a derived design of a symmetric design as block matrices with each block being a zero matrix or an incidence matrix of a smaller residual or derived design, respectively. 相似文献
16.
It is shown that for each λ ? 3, there are only finitely many quasi-residual quasi-symmetric (QRQS) designs and that for each pair of intersection numbers (x, y) not equal to (0, 1) or (1, 2), there are only finitely many QRQS designs.A design is shown to be affine if and only if it is QRQS with x = 0. A projective design is defined as a symmetric design which has an affine residual. For a projective design, the block-derived design and the dual of the point-derivate of the residual are multiples of symmetric designs. 相似文献
17.
It is shown that a partial geometric design with parameters (r, k, t, c) satisfying certain conditions is equivalent to a two-class partially balanced incomplete block design. This generalizes a result concerning partial geometric designs and balanced incomplete block designs. 相似文献
18.
Sven Hartmann 《组合设计杂志》2002,10(4):239-255
A digraph design is a decomposition of a complete (symmetric) digraph into copies of pre‐specified digraphs. Well‐known examples for digraph designs are Mendelsohn designs, directed designs or orthogonal directed covers. A digraph design is superpure if any two of the subdigraphs in the decomposition have no more than two vertices in common. We give an asymptotic existence theorem for superpure digraph designs, which is a variation of an earlier result of Lamken and Wilson J Combin Theory Ser A 89: 149–200, 2000. As an immediate consequence, we obtain new results for supersimple designs and pure perfect Mendelsohn designs. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 239–255, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10013 相似文献
19.
Motivated by an application to sensor networks, Lee and Stinson [ 6 ] defined a new type of set system termed a “common intersection design.” Briefly, a µ‐common intersection design is a 1‐design in which no pair of points occurs in more than one block, and in which any two disjoint blocks intersect at least µ blocks in common. In general, we want to maximize µ as a function of the other parmameters of the design. In this paper, we analyze combinatorial properties of common intersection designs. We determine necessary conditions for “optimal” common intersection designs and provide several existence results. Connections with other types of designs are pointed out. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 251–269, 2006 相似文献
20.
Joe Masaro 《Linear algebra and its applications》2008,429(7):1639-1646
Suppose that Y = (Yi) is a normal random vector with mean Xb and covariance σ2In, where b is a p-dimensional vector (bj), X = (Xij) is an n × p matrix with Xij ∈ {−1, 1}; this corresponds to a factorial design with −1, 1 representing low or high level respectively, or corresponds to a weighing design with −1, 1 representing an object j with weight bj placed on the left and right of a chemical balance respectively. E-optimal designs Z are chosen that are robust in the sense that they remain E-optimal when the covariance of Yi, Yi′ is ρ > 0 for i ≠ i′. Within a smaller class of designs similar results are obtained with respect to a general class of optimality criteria which include the A- and D-criteria. 相似文献