-optimal designs for quadratic mixture canonical polynomials with spline

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

10.31274/rtd-180813-13130 ◽

1984 ◽

Author(s):

Moun-Shen Carl Lee

Keyword(s):

Optimal Designs

Faculty Opinions recommendation of Optimal designs for two-stage genome-wide association studies.

Faculty Opinions – Post-Publication Peer Review of the Biomedical Literature ◽

10.3410/f.1087330.540352 ◽

2007 ◽

Author(s):

Jurg Ott

Keyword(s):

Association Studies ◽

Genome Wide Association ◽

Optimal Designs ◽

Genome Wide Association Studies ◽

Two Stage ◽

Genome Wide

A Collection of A-Optimal Designs for Control-Test Treatment Comparisons. I.

10.21236/ada129322 ◽

1983 ◽

Author(s):

A. S. Hedayat ◽

D. Majumdar

Keyword(s):

Optimal Designs ◽

Control Test ◽

Treatment Comparisons ◽

Test Treatment

Ensemble Techniques for Determining Globally Optimal Designs for Problems with Broadly Stated Design Objectives

10.21236/ada483964 ◽

2008 ◽

Author(s):

Chunming Wang ◽

Gary I. Rosen

Keyword(s):

Optimal Designs ◽

Ensemble Techniques

Dynamic modeling and power optimization of a 4RPSP+PS parallel flight simulator machine

Robotica ◽

10.1017/s0263574721000746 ◽

2021 ◽

pp. 1-26

Author(s):

Soheil Zarkandi

Keyword(s):

Power Consumption ◽

Dynamic Modeling ◽

Parallel Manipulator ◽

Degrees Of Freedom ◽

Pareto Front ◽

Essential Role ◽

Power Optimization ◽

Optimal Designs ◽

Flight Simulator ◽

Lagrange Method

Abstract Reducing consumed power of a robotic machine has an essential role in enhancing its energy efficiency and must be considered during its design process. This paper deals with dynamic modeling and power optimization of a four-degrees-of-freedom flight simulator machine. Simulator cabin of the machine has yaw, pitch, roll and heave motions produced by a 4RPSP+PS parallel manipulator (PM). Using the Euler–Lagrange method, a closed-form dynamic equation is derived for the 4RPSP+PS PM, and its power consumption is computed on the entire workspace. Then, a newly introduced optimization algorithm called multiobjective golden eagle optimizer is utilized to establish a Pareto front of optimal designs of the manipulator having a relatively larger workspace and lower power consumption. The results are verified through numerical examples.

Asymptotic Inference for Optimal Rerandomization Designs

Open Statistics ◽

10.1515/stat-2020-0102 ◽

2021 ◽

Vol 1 (1) ◽

pp. 49-58

Author(s):

Mårten Schultzberg ◽

Per Johansson

Keyword(s):

Experimental Design ◽

Normal Distribution ◽

Mahalanobis Distance ◽

Design Strategy ◽

Sampling Distribution ◽

Optimal Designs ◽

Asymptotic Inference ◽

Optimal Allocations ◽

Asymptotic Sampling

AbstractRecently a computational-based experimental design strategy called rerandomization has been proposed as an alternative or complement to traditional blocked designs. The idea of rerandomization is to remove, from consideration, those allocations with large imbalances in observed covariates according to a balance criterion, and then randomize within the set of acceptable allocations. Based on the Mahalanobis distance criterion for balancing the covariates, we show that asymptotic inference to the population, from which the units in the sample are randomly drawn, is possible using only the set of best, or ‘optimal’, allocations. Finally, we show that for the optimal and near optimal designs, the quite complex asymptotic sampling distribution derived by Li et al. (2018), is well approximated by a normal distribution.