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1.
The optimality of designs obtained by adding p runs to an orthogonal array is studied for experiments involving m factors each at s levels. The optimality criterion used here, is the Type 1 criterion due to Cheng (1978) which is an extension of Kiefer (1975)
universal optimality criterion. Unlike what happens with orthogonal array plus one run designs, the behavior of designs obtained
via augmentation of an orthogonal array by p runs depends on the particular runs added. 相似文献
2.
Lower bounds of various discrepancies on combined designs 总被引:1,自引:0,他引:1
The foldover is a useful technique in construction of two-level factorial designs. A foldover design is the follow-up experiment
generated by reversing the sign(s) of one or more factors in the initial design. The full design obtained by joining the runs
in the foldover design to those of the initial design is called the combined design. In this paper, some lower bounds of various
discrepancies of combined designs, such as centered L
2-discrepancy, symmetric L
2-discrepancy and wrap-around L
2-discrepancy, under a general foldover plan are obtained, which can be used as a benchmark for searching optimal foldover
plans. Our results provide a theoretical justification for optimal foldover plans in terms of uniformity criterion. 相似文献
3.
Combined-optimal designs (Li and Lin, 2003) are obviously the best choices for the initial designs if we partition the experiment
into two parts with equal size to obtain some information about the process, especially for the case not considering the blocking
factor. In this paper, the definition of combined-optimal design is extended to the case when blocking factor is significant,
and this new class of designs is called blocked combined-optimal designs. Some general results are obtained which relate 2k−pIII initial designs with their complementary designs when , where n=2k−p. By applying these results, we are able to characterize 2k−pIII combined-optimal designs or blocked combined-optimal designs in terms of their complementary designs. It is also proved that
both 2k−pIII combined-optimal and blocked combined-optimal designs are not minimum aberration designs when and n−1−k > 2. And some combined-optimal and blocked combined-optimal designs with 16 and 32 runs are constructed for illustration.
2000 Mathematics Subject Classifications: 62K15, 62K05 相似文献
4.
This paper studies minimally-supported D-optimal designs for polynomial regression model with logarithmically concave (log-concave) weight functions. Many commonly
used weight functions in the design literature are log-concave. For example,
and exp(−x
2) in Theorem 2.3.2 of Fedorov (Theory of optimal experiments, 1972) are all log-concave. We show that the determinant of information
matrix of minimally-supported design is a log-concave function of ordered support points and the D-optimal design is unique. Therefore, the numerically D-optimal designs can be constructed efficiently by cyclic exchange algorithm. 相似文献
5.
We consider the problem of comparison of one test treatment (τ0) with a set of v control treatments (τ1, τ2, …, τv) using distance optimality [DS-optimality] criterion introduced by Sinha (1970) in some treatment-connected design settings.
It turns out that the nature of DS-optimal designs is quite similar to that for the usual A−, D− and E− optimality criteria. However, the optimality problem is quite complicated in most situations. First we deal with the CRD
model and derive DS-optimal allocations for a given set of treatments. The results are almost identical to the A-optimal allocations
for such problems. Then we consider a block design set-up and examine the nature of DS-optimal designs. In the process, we
introduce the method of weighted coverage probability and maximize the resulting expression to obtain an optimal design.
Received: December 1999 相似文献
6.
This paper deals with Bayesian design over U-type designs of n runs and s factors with q levels for nonparametric response surface prediction. The criterion is developed in terms of the asymptotic approach of Mitchell
et al. (Ann Statist 22: 634–651, 1994) for a specific covariance kernel. An optimal design is given in approximate design
theory over the all level combinations. A connection with orthogonality and aberration is established. A lower bound for the
criterion is provided, and numerical results show that this lower bound is tight. 相似文献
7.
Asymmetrical Factorial Designs Containing Clear Effects 总被引:1,自引:0,他引:1
The asymmetrical or mixed-level factorial design is a kind of important design in practice. There is a natural problem on how to choose an optimal (s
2)s
n
design for the practical need, where s is any prime or prime power. This paper considers the clear effects criterion for selecting good designs. It answers the questions of when an (s
2)s
n
design with fixed number of runs contains clear two-factor interaction (in brief 2fi) components and when it contains clear main effects or clear 2fis. It further gives the complete classification of (s
2)s
n
designs according to the clear 2fi components, main effects and 2fis they have. 相似文献
8.
Holger Dette 《Metrika》1997,46(1):71-82
In his book Pukelsheim [8] pointed out that designs supported at the arcsin points are very efficient for the statistical
inference in a polynomial regression model. In this note we determine the canonical moments of a class of distributions which
have nearly equal weights at the arcsin points. The class contains theD-optimal arcsin support design and theD
1-optimal design for a polynomial regression. The results allow explicit representations ofD-, andD
1-efficiencies of these designs in all polynomial models with a degree less than the number of support points of the design. 相似文献
9.
In this paper we consider the exact D-optimal designs for estimation of the unknown parameters in the two factors, each at only two-level, main effects model with autocorrelated errors. The vector of the n random errors in the observed responses is assumed to follow a first-order autoregressive model (AR(1)). The exact D-optimal designs seek the optimal combinations of the design levels as well as the optimal run orders, so that the determinant of the information matrix of BLUEs for the unknown parameters is maximized. Bora-Senta and Moyssiadis (1999) gave some conjectures about the exact D-optimal designs based on their experience of several exhaustive searches. In this paper their conjectures are partially proved to be true.Received: January 2003 / Accepted: October 2003Partially supported by the National Science Council of Taiwan, R.O.C. under grant NSC 91-2115-M-008-013.Supported in part by the National Science Council of Taiwan, R.O.C. under grant NSC 89-2118-M-110-003. 相似文献
10.
Screening designs are useful for situations where a large number of factors are examined but only a few, k, of them are expected to be important. Traditionally orthogonal arrays such as Hadamard matrices and Plackett Burman designs have been studied for this purpose. It is therefore of practical interest for a given k to know all the classes of inequivalent projections of the design into the k dimensions that have certain statistical properties. In this paper we present 15 inequivalent Hadamard matrices of order n=32 constructed from circulant cores. We study their projection properties using several well-known statistical criteria and we provide minimum generalized aberration 2 level designs with 32 runs and up to seven factors that are embedded into these Hadamard matrices. A concept of generalized projectivity and design selection of such designs is also discussed.AMS Subject Classification: Primary 62K15, Secondary 05B20 相似文献
11.
The theory of unimodular matrices has been applied to deriveD-optimal main effect plans fors
1 ×s
2 factorials ins
1 +s
2 runs. Plans with highA-efficiency have also been given. 相似文献
12.
Stelios D. Georgiou 《Metrika》2008,68(2):189-198
Supersaturated designs are an important class of factorial designs in which the number of factors is larger than the number
of runs. These designs supply an economical method to perform and analyze industrial experiments. In this paper, we consider
generalized Legendre pairs and their corresponding matrices to construct E(s
2)-optimal two-level supersaturated designs suitable for screening experiments. Also, we provide some general theorems which
supply several infinite families of E(s
2)-optimal two-level supersaturated designs of various sizes.
相似文献
13.
Optimal mixed-level supersaturated design 总被引:6,自引:1,他引:6
A supersaturated design is essentially a fractional factorial in which the number of potential effects is greater than the number of runs. In this paper, E(f
NOD
) criterion is employed for comparing supersaturated designs from the viewpoint of orthogonality and uniformity, and a lower bound of E(f
NOD
) which can serve as a benchmark of design optimality is obtained. It is shown that the existing E(s
2) and ave 2 criteria (for two- and three-level supersaturated designs respectively) are in fact special cases of this criterion. Furthermore, a construction method for mixed-level supersaturated designs is proposed and some properties of the resulting designs are investigated.
Key words:Discrepancy; Hamming distance; Orthogonal array; Supersaturated design; Uniformity; U-type design.
2000 Mathematics Subject Classifications62K15, 62K05, 62K99.
Corresponding author. 相似文献
14.
A mixture experiment is an experiment in which the k ingredients are nonnegative and subject to the simplex restriction on the (k − 1)-dimensional probability simplex S
k-1. In this work, an essentially complete class of designs under the Kiefer ordering for a linear log contrast model with a
mixture experiment is presented. Based on the completeness result, -optimal designs for all p,−∞ ≤ p ≤ 1 including D- and A-optimal are obtained, where the eigenvalues of the design moment matrix are used. By using the approach presented here, we
gain insight on how these -optimal designs behave.
Mong-Na Lo Huang was supported in part by the National Science Council of Taiwan, ROC under grant NSC 93-2118-M-110-001. 相似文献
15.
This paper investigates the robustness of variance-balanced row-column designs for complete diallel cross experiments for
estimating the comparisons among the general combining ability parameters against the loss of observations. A necessary and
sufficient condition of robustness as per connectedness criterion is obtained. The robustness of optimal row-column designs
of Gupta and Choi (1998) has been investigated for the loss of any m(≥1) observations in a column and for the loss of any two observations in the design. The study of robustness has also been
conducted as per A-efficiency criterion. 相似文献
16.
Luc Pronzato 《Metrika》2010,71(2):219-238
We study the consistency of parameter estimators in adaptive designs generated by a one-step ahead D-optimal algorithm. We show that when the design space is finite, under mild conditions the least-squares estimator in a nonlinear
regression model is strongly consistent and the information matrix evaluated at the current estimated value of the parameters
strongly converges to the D-optimal matrix for the unknown true value of the parameters. A similar property is shown to hold for maximum-likelihood estimation
in Bernoulli trials (dose–response experiments). Some examples are presented. 相似文献
17.
Screening designs are useful for situations where a large number of factors (q) is examined but only few (k) of these are expected to be important. It is of practical interest for a given k to know all the inequivalent projections of the design into the k dimensions. In this paper we give all the (combinatorially) inequivalent projections of inequivalent Hadamard matrices of order 24 into k=3,4 and 5 dimensions, as well as their frequencies. Then, we sort these projections according to their generalized resolution, generalized aberration and centered L2-discrepancy measure of uniformity. Then, we study the hidden projection properties of these designs as they are introduced by Wang and Wu (1995). The hidden projection property suggests that complex aliasing allows some interactions to be estimated without making additional runs. 相似文献
18.
Holger Dette 《Metrika》1993,40(1):37-50
The optimal design problem for the estimation of several linear combinationsc′
l
ϑ (l=1, …,m) is considered in the usual linear regression modely=f′(x)ϑ (f(x) ∈ ℝ
k
,ϑ ∈ ℝ
k
). An optimal design minimizes a (weighted)p-norm of the variances of the least squares estimates for the different linear combinationsc′
l
ϑ. A generalized Elfving theorem is used to derive the relation of the new optimality criterion to theE-optimal design problem. It is shown that theE-optimal design for the parameterϑ minimizes such a (weighted)p-norm whenever the vectorc=(c′
1, …, c′k)′ is an inball vector of a symmetric convex and compact “Elfving set” in. 相似文献
19.
In this paper we construct all possible orthogonal arrays OA(18,q, 3,2) with 18 runs and 3 ≤ q ≤ 7 columns and present those that are nonisomorphic. A discussion on the novelty and the superiority of many of the designs
found in terms of isomorphism and generalized minimum aberration has been made.
相似文献
20.
Consider the design problem for the approximately linear model with serially correlated errors. The correlated structure is
the qth degree moving average process, MA(q), especially for q = 1, 2. The optimal design is derived by using Bayesian approach. The Bayesian designs derived with various priors are compared
with the classical designs with respect to some specific correlated structures. The results show that any prior knowledge
about the sign of the MA(q) process parameters leads to designs that are considerately more efficient than the classical ones based on homoscedastic
assumptions. 相似文献