论文信息 - Nearly Trend-Free Block Designs

Nearly Trend-Free Block Designs

Abstract Trend-free block designs were developed to permit elimination of effects of low-order components of common within-block trends over experimental units. It is known that, for certain combinations of design parameters, trend-free block designs do not exist. In this article, concepts and properties of nearly trend-free block designs are presented in general, and complete block designs with linear or quadratic trends over plots within blocks are studied in particular. It is found that, under a linear trend, if trend-free complete block designs do not exist, nearly trend-free block designs can be constructed and they are A- and D-optimal. When the trend is quadratic, highly efficient designs can be obtained.

[1] W. T. Federer,et al. The Use of Covariance to Control Gradients in Experiments , 1954 .

[2] I. Olkin,et al. Inequalities: Theory of Majorization and Its Applications , 1980 .

[3] J. Kiefer. Optimum Experimental Designs , 1959 .

[4] Ralph A. Bradley,et al. Trend-Free Block Designs: Theory. , 1980 .

[5] J. Kiefer. ON THE NONRANDOMIZED OPTIMALITY AND RANDOMIZED NONOPTIMALITY OF SYMMETRICAL DESIGNS , 1958 .

[6] Changbao Wu,et al. Balanced Repeated Measurements Designs , 1980 .

[7] Calyampudi Radhakrishna Rao,et al. Linear Statistical Inference and its Applications , 1967 .

[8] Ralph A. Bradley,et al. Trend-free block designs: existence and construction results , 1983 .