X⁻¹-balance of some partially balanced experimental designs with particular emphasis on block and row-column designs

• Autorzy: Ryszard Walkowiak
• Języki publikacji: EN

Abstrakty

EN

This paper considers block designs and row-column designs where the information matrix C has two different nonzero eigenvalues, one of multiplicity 1 and the other of multiplicity h−1, where h is the rank of the matrix C. It was found that for each such design there exists a diagonal positive definite matrix X such that the design is X −1-balanced.

Słowa kluczowe

EN

block design; row-column design; efficiency balance; variance balance; X−1-balance

• Wydawca: De Gruyter Open
• Czasopismo: Biometrical Letters
• Rocznik: 2015
• Tom: 52
• Numer: 1
• Strony: 1-12

Daty

wydano

2015-06-01

online

2015-06-08

Twórcy

autor

Ryszard Walkowiak

• Department of Mathematical and Statistical Methods, Poznan University of Life Sciences, Wojska Polskiego 28, 60-637 Poznań, Poland

Bibliografia

• Caliński T. (1977): On the notion of balance in block designs. Recent Developments in Statistics, North-Holland Publishing Company.
• Clatworthy W.H. (1973): Tables of Two-Associate Class Partially Balanced Designs. Applied Mathematics Series 63, National Bureau of Standards, Washington.
• Gupta S., Kageyama S. (1993): Type S designs in unequal blocks. Journal of Combinatorics, Information & System Sciences 18(1-2): 97-112.
• Nigam A.K. (1976): On some balanced row-and-column designs. Sankhya B38: 87-91.
• Pearce S.C. (1960): Supplemented balance. Biometrica 47(3&4): 263-271.[Crossref]
• Pearce S.C. (1975): Row and column designs. Appl. Statist. 24: 60-74.
• Pearce S. C., Caliński T., Marshall T. F. de C. (1974): The basic contrasts of an experimental designs with special reference to the analysis of data. Biometrika 61: 449-460.[Crossref]
• Raghavarao O., Federer W.T. (1975): On connectedness in two-way elimination of heterogeneity designs. Ann. Statist. 3: 730-735.
• Rao C.R., Mitra S.K. (1971): Generalized inverse of matrices and its applications. New York, Wiley.

Identyfikatory

DOI

10.1515/bile-2015-0001