ﻻ يوجد ملخص باللغة العربية
In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal criteria, $D$- and $A$-optimal criteria. For $D$-optimality, we provide an alternative proof for the monotonic convergence for $D$-optimal criterion and propose an efficient computational algorithm to obtain the approximate $D$-optimal design. We further show that the proposed algorithm converges to the $D$-optimal design, and then prove that the approximate $D$-optimal design converges to the continuous $D$-optimal design under certain conditions. For $A$-optimality, we provide an efficient algorithm to obtain approximate $A$-optimal design and conjecture the monotonicity of the proposed algorithm. Numerical comparisons suggest that the proposed algorithms perform well and they are comparable or superior to some existing algorithms.
Supersaturated design (SSD) has received much recent interest because of its potential in factor screening experiments. In this paper, we provide equivalent conditions for two columns to be fully aliased and consequently propose methods for construct
In this note we consider the optimal design problem for estimating the slope of a polynomial regression with no intercept at a given point, say z. In contrast to previous work, which considers symmetric design spaces we investigate the model on the i
We develop $D$-optimal designs for linear models with first-order interactions on a subset of the $2^K$ full factorial design region, when both the number of factors set to the higher level and the number of factors set to the lower level are simulta
The minimum aberration criterion has been frequently used in the selection of fractional factorial designs with nominal factors. For designs with quantitative factors, however, level permutation of factors could alter their geometrical structures and
For a joint model-based and design-based inference, we establish functional central limit theorems for the Horvitz-Thompson empirical process and the Hajek empirical process centered by their finite population mean as well as by their super-populatio