Optimal Designs in the Presence of Random Block Effects

2002 ◽  
pp. 103-138
Author(s):  
Peter Goos
Keyword(s):  
Optimal Designs ◽  
Random Block

Q-optimal experimental designs and close to them experimental designs for polynomial regression on the interval

2020 ◽  
Vol 86 (5) ◽  
pp. 65-72
Author(s):  
Yu. D. Grigoriev
Keyword(s):  
Optimal Design ◽  
Polynomial Regression ◽  
Direct Consequence ◽  
Experimental Designs ◽  
Optimal Designs ◽  
Software Systems ◽  
General Character ◽  
Support Points ◽  
Optimal Weights ◽  
Universal Expression

The problem of constructing Q-optimal experimental designs for polynomial regression on the interval [–1, 1] is considered. It is shown that well-known Malyutov – Fedorov designs using D-optimal designs (so-called Legendre spectrum) are other than Q-optimal designs. This statement is a direct consequence of Shabados remark which disproved the Erdős hypothesis that the spectrum (support points) of saturated D-optimal designs for polynomial regression on a segment appeared to be support points of saturated Q-optimal designs. We present a saturated exact Q-optimal design for polynomial regression with s = 3 which proves the Shabados notion and then extend this statement to approximate designs. It is shown that when s = 3, 4 the Malyutov – Fedorov theorem on approximate Q-optimal design is also incorrect, though it still stands for s = 1, 2. The Malyutov – Fedorov designs with Legendre spectrum are considered from the standpoint of their proximity to Q-optimal designs. Case studies revealed that they are close enough for small degrees s of polynomial regression. A universal expression for Q-optimal distribution of the weights pi for support points xi for an arbitrary spectrum is derived. The expression is used to tabulate the distribution of weights for Malyutov – Fedorov designs at s = 3, ..., 6. The general character of the obtained expression is noted for Q-optimal weights with A-optimal weight distribution (Pukelsheim distribution) for the same problem statement. In conclusion a brief recommendation on the numerical construction of Q-optimal designs is given. It is noted that in this case in addition to conventional numerical methods some software systems of symbolic computations using methods of resultants and elimination theory can be successfully applied. The examples of Q-optimal designs considered in the paper are constructed using precisely these methods.

Constrained optimal designs

1984 ◽  
Author(s):  
Moun-Shen Carl Lee
Keyword(s):  
Optimal Designs

THE IMPACT OF MINERAL FERTILIZERS ON THE BIOLOGICAL YIELD OF SUGAR BEET CROP (BETA VULGARIS L. VAR. SACCHARIFERA)

2018 ◽  
Vol 28 (4) ◽  
pp. 1281-1284
Author(s):  
Petar Petrov ◽  
Bojan Mitrovski
Keyword(s):  
Sugar Beet ◽  
Field Trials ◽  
Mineral Fertilizers ◽  
Qualitative Properties ◽  
New Production ◽  
Economic Significance ◽  
Random Block ◽  
Biological Yield ◽  
Sugar Beet Crop ◽  
The Impact

Due to the great economic significance of the sugar beet, the new production trends are aimed at improving the quantitative and qualitative properties and one of the basic agro technical measures that is directly dependent on the yield and quality of the turnip is the properly conducted plant nutrition. Exporting high quantities of nutrients from the soil, the sugar beet requires application of advanced agro-technology, primarily application of adequate and controlled nutrition and irrigation. Application of this measure, in combination with soil processing, has sustained influence over the following cultures in the crop rotation in terms of nutrients regiment and fight against weeds.In order to determine the effects of mineral fertilizers on sugar beet, field experiment was conducted on fluvisol soil. The experiment is set according to a random block system, following the standard methods of agricultural chemistry for conducting field trials. The experiment includes eight variants, as follows: 1. Control (non-fertilized), 2. NP, 3. NK, 4. PK, 5. NPK, 6. N2PK, 7. N2P2K, 8. N3PK.In the phase of technological maturity of sugar beet, collection of the vegetative material and measurement of the height of the biological yield of the turnips was carried out. Based on the survey results, it can be concluded that the variant N2P2K has achieved the highest yield of swollen roots, i.e. 69.330 kg/ha. The highest yield of leafy greens was achieved in the variant N3PK, i.e. 41.920 kg/ha, which indicates the fact that nitrogen has direct influence over the vegetation mass of sugar beet.

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