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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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A unified terminology in block designs

100%
Caliński T., Kageyama S.
Discussiones Mathematicae Probability and Statistics
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2004
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tom 24
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nr 1
127-145
EN
Partially efficiency balanced (PEB) designs with m efficiency classes have been defined by Puri and Nigam [15] as block designs which have simple analysis and, if properly used, allow the important contrasts to be estimated with desired efficiency. Such designs can be made available in varying replications and/or unequal block sizes. However, any block design is a PEB design with m efficiency classes for some m < v, where v is the number of treatments in the design. So the term "PEB" itself is not much informative in a statistical sense. More information may be added to this term. In this paper, a unified terminology is suggested, aimed at giving more statistical meaning to the PEB designs, which may or may not be connected. The paper is essentially based on our recent books "BLOCK DESIGNS: A Randomization Approach", Springer Lecture Notes in Statistics, Vol. 150 (2000), Vol. 170 (2003), with some new additions.
2
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Two open problems on balanced block designs

99%
Kageyama S.
Banach Center Publications
|
1989
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tom 25
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nr 1
113-118
3
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Certain new M-matrices and their properties with applications

81%
Mohan R., Kageyama S., Lee M., Yang G.
Discussiones Mathematicae Probability and Statistics
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2008
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tom 28
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nr 2
183-207
EN
The Mₙ-matrix was defined by Mohan [21] who has shown a method of constructing (1,-1)-matrices and studied some of their properties. The (1,-1)-matrices were constructed and studied by Cohn [6], Ehrlich [9], Ehrlich and Zeller [10], and Wang [34]. But in this paper, while giving some resemblances of this matrix with a Hadamard matrix, and by naming it as an M-matrix, we show how to construct partially balanced incomplete block designs and some regular graphs by it. Two types of these M-matrices have been considered. Also we will make a mention of certain applications of these M-matrices in signal and communication processing, and network systems and end with some open problems.
4
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Some constructions of nested balanced equireplicate block designs

81%
Rai S., Banerjee S., Kageyama S.
Discussiones Mathematicae Probability and Statistics
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2003
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tom 23
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nr 1
45-68
EN
arious methods of constructing nested ternary and quaternary efficiency balanced and variance balanced designs are proposed by applying some repetitions of treatments in all possible pairs of treatments. In these designs sub-blocks and super-blocks may form different p-ary designs, where sub-blocks have higher efficiency as compared to super-blocks, i.e., any two elementary treatment contrasts in the sub-blocks can be measured with higher efficiency than any two elementary contrasts in the super-block structure. A comparison is shown in Table 1.
5
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Some observations on the constructions of chemical balance weighing designs

81%
Mohan R., Ceranka B., Kageyama S.
Discussiones Mathematicae Probability and Statistics
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2001
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tom 21
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nr 2
99-110
EN
The construction of some optimum chemical balance weighing designs from affine μ-resolvable balanced incomplete block (BIB) designs are discussed in the light of a characterization theorem on the parameters of affine μ-resolvable BIB designs as given by Mohan and Kageyama (1982), for the sake of practical use of researchers who need some selective designs for the construction of chemical balance weighing designs.
6
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On a characterization of symmetric balanced incomplete block designs

81%
Mohan R., Kageyama S., Nair M.
Discussiones Mathematicae Probability and Statistics
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2004
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tom 24
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nr 1
41-58
EN
All the symmetric balanced incomplete block (SBIB) designs have been characterized and a new generalized expression on parameters of SBIB designs has been obtained. The parameter b has been formulated in a different way which is denoted by bi, i = 1, 2, 3, associating with the types of the SBIB design Di. The parameters of all the designs obtained through this representation have been tabulated while corresponding them with the suitable formulae for the number ofblocks bi and the expression Si for the convenience of practical users for constructional methods of certain designs, which is the main theme of this paper.
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