A note on the robustness of Box-Behnken designs to the unavailability of data

Box-Behnken designs and central composite designs are efficient designs for fitting second order polynomials to response surfaces, because they use relatively small numbers of observations to estimate the parameters. In this paper we investigate the robustness of Box-Behnken designs to the unavailability of observations, in the sense of finding t _max , the maximum number of arbitrary rows in the design matrix that can be removed and still leave all of the parameters of interest estimable. The results are compared to the known results for the central composite designs found in MacEachern, Notz, Whittinghill & Zhu (1995). The blocked Box-Behnken designs are equally as robust as those that are not blocked. Received December 1997     

A note on connectedness of block designs

Summary We give a simple proof for the well known result that a block design (for an additive, fixed effects block model withv treatments inb blocks) is connected iff its ℰ-matrix has rankv-1.     

On recursive construction for balanced incomplete block designs with nested rows and columns

This paper presents a recursive method for the construction of balanced incomplete block designs with nested rows and columns.     

Robustness of Williams Square change-over designs

In literature, Williams Square change-over designs balanced for first residual effects of treatments have been proved to be universally optimal. Here, an attempt has been made to show that these designs are robust against missing of last α [≤v−1; v being the number of periods in the design for v treatments] observations from an experimental unit. Received May 2000     

Optimal extended complete block designs for dependent observations

Optimal designs under general dependence structures are usually difficult to specify theoretically or find algorithmically. However, they can sometimes be found for a specific dependence structure and a particular parameter value. In this paper, a class of generalized binary block designs with t treatments and b blocks of size k>t is considered. Each block consists of h consecutive complete blocks and, at the end, an incomplete block of size k−ht (if k > ht). For a suitable number of blocks, a universally optimal design is found for a first-order stationary autoregressive process with positive correlations. Optimal generalized binary designs and balanced block designs are also considered. Some constructions for a universally optimal design are described. A negative dependence parameter, and some other dependence structures, are also considered.     

Nested balancedN-ary designs

Nested balancedn-ary designs are introduced. Some methods of construction of such designs are presented with some series of designs.     

Construction of block designs admitting an Abelian automorphism group

Construction of block designs admitting an action of a presumed automorphism group consists of two basic steps: 1.construction of orbit structures for the given automorphism group, 2. construction of block designs for the orbit structures obtained in 1. For an abelian group G, the second step, called indexing, often lasts too long, because there are too many possibilities to be enumerated with today's computer facilities. To make such a construction possible we use a principal series of the group G to obtain a refinement of the orbit structures.     

A series of resolvable PBIB(3) designs with two replicates

A new series of resolvable PBIB(3) designs with two replications has been proposed along with a simple method of analysis. These designs form a generalization of circular lattice designs of Rao (1956).     

On the E-optimality of truncated block designs

Sufficient conditions are found for designs, derived from completely symmetric designs by deleting binary blocks, to be E-optimal. Sufficient conditions are also found for E-optimality of designs obtained from other E-optimal designs by deleting all blocks forming a balanced incomplete block design on a subset of the treatments. The results include many binary and non-binary designs for which E-optimality was previously unknown.     

地铁列车初始布点的鲁棒性研究

针对车辆段内干扰源对地铁列车运行的扰动,以列车连带晚点期望值最小为目标,确定地铁列车平峰时段的始发时刻,分配初始缓冲时间。细分连带晚点,详细描述了连带晚点传播的各种情况,建立了简单情形下地铁列车初始布点的理论模型。经分析,该模型为凸规划的约束极值问题,且证明在小干扰条件下,均衡初始布点的列车时刻表为模型的最优解。     

Optimality of block designs with variable block sizes and random block effects

We consider the simple block model with random block effects, the block effects having variance _b ² =²;, with ² the variance of the errors. It is assumed that the experimenter can vary the sizes of the blocks. The universal optimality of certain designs for all over all designs with the same number of blocks and the same number of observations is shown. It is of interest to note that if Balanced Incomplete Block Designs compete, then they perform equally well for =0 and for =, i.e. in the one way classification model and in the simple block model with fixed block effects, but they perform worse for every (0, ).The result is, however, theoretical in nature. It treats a situation which is not very likely to happen in practice. The interest lies in the fact that it provides a counterexample to a conjecture on optimality of designs in mixed models.     

On Long-term Forecasting of Social Security: A Robustness Analysis

In this paper we present a macro-economic demographic growth modelhaving a special focus on social security. It is designed to study the variability of responses of the system in presence of risks and uncertainties. Here we analyze the robustness of the model towards uncertainties in parameterspecifications, introduced by ARCH-M models with the incorporation ofintervention processes. The parameters varied are labor force participationrates (one of the key sources of uncertainty in the social security policydebate), and the parameters of the production function (the key source ofuncertainty in any long-run economic analysis). The sensitivity analysisfocuses on two variables: assets of the private pension system and thebalance of the public `Pay As You Go' pension system. Special attentionis given to convergence properties of the macro-economic model.     

TypeS designs with nested rows and columns

Summary Supplemented balance in block designs with nested rows and columns is considered, under the name of typeS designs with nested rows and columns. Analysis and construction of such designs are also discussed.     

A note on theE-optimality of block designs

Summary In this paper we consider the problem of determiningE-optimal block designs for experimental situations in whichv treatments are to be tested onn experimental units arranged inb blocks and where the block sizes and number of replications assigned to the treatments are allowed to vary. Some sufficient conditions are obtained for designs to beE-optimal in these situations and methods for constructing designs which satisfy the sufficient conditions given are also derived.     

On the application of the Minkowski-Farkas theorem to sampling designs

In the paper, we consider the following problem: Let {π_k} be a sequence satisfying 0π_kΣ1 (k=1,…, N) and π=n.Tben, is there an unordered sampling design such that, for each k=1,…N, the inclusion probability of unit k is equal to π? It is shown that it can be solved by the straightforward application of the Minkowski-Farkas theorem.     

Qualitative Robustness of S*-estimators of Multivariate Location and Dispersion

S-estimators of multivariate location and dispersion are favored for their robustness against outliers. The computations of the exact S -estimators, however, are difficult, if not impossible. We consider S*-estimators, a variant of the S-estimators which is commonly computed in reality. It is shown under very general conditions that S*-estimators are qualitatively robust with respect to a wide range of metrics, including Prohorov metric and a weak affine invariant metric based on Vapnik-Cervonenkis sets. The result follows from a continuity result of the S*-functionals and almost everywhere continuity result of the corresponding estimators in finite-sample cases.     

Choice of optimal initial designs in sequential experiments

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 2^k−p_III initial designs with their complementary designs when , where n=2^k−p. By applying these results, we are able to characterize 2^k−p_III combined-optimal designs or blocked combined-optimal designs in terms of their complementary designs. It is also proved that both 2^k−p_III 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     

A typology of mixed methods research designs

The mixed methods paradigm is still in its adolescence, and, thus, is still relatively unknown and confusing to many researchers. In general, mixed methods research represents research that involves collecting, analyzing, and interpreting quantitative and qualitative data in a single study or in a series of studies that investigate the same underlying phenomenon. Over the last several years, a plethora of research designs have been developed. However, the number of designs that currently prevail leaves the doctoral student, the beginning researcher, and even the experienced researcher who is new to the field of mixed methods research with the challenge of selecting optimal mixed methods designs. This paper presents a three-dimensional typology of mixed methods designs that represents an attempt to rise to the challenge of creating an integrated typology of mixed methods designs. An example for each design is included as well as a notation system that fits our eight-design framework. This paper won the James E. McLean outstanding paper award.     

基于复杂多响应相关性的稳健性优化设计

本文对目前复杂多响应问题中,响应间相关性复杂问题的稳健性优化设计方法进行了分析和总结,考察了2种复杂多响应的稳健优化技术,比较了各种方法的特点同时又考虑了稳健性满意度函数法,并对其进行了优化。研究结果表明,最优化稳健性满意度函数法能够很好的平衡复杂多响应中的优化与稳健性的问题,可以很好的解决现代工业产品中只考虑最优化忽略稳定性而导致"召回门"不断的问题。     

Analysis of treatment response data from eligibility designs

In this paper, we develop and compare two alternative approaches for calculating the effect of the actual intake when treatments are randomized, but compliance with the assignment in the treatment arm is less than perfect for reasons that are correlated with the outcome. The approaches are based on different identification assumptions about these unobserved confounders. In the first approach, which stems from [Sommer, A., Zeger, S., 1991. On estimating efficacy in clinical trials. Statistics in Medicine 10, 45–52], the unobserved confounders are modeled by a discrete indicator variable that represents subject-type, defined in terms of the potential intake in the face of each possible assignment. In the second approach, confounding is modeled without reference to subject-type in the spirit of the Roy model. Because the two models are non-nested, and model comparison and assessment of the approaches in a real data setting is one of our central goals, we formulate the discussion from a Bayesian perspective, comparing the two models in terms of marginal likelihoods and Bayes factors, and in terms of inferences about the treatment effects. The latter we calculate from a predictive perspective in a way that is different from that in the literature, where typically only a point summary of that effect is calculated. Our real data analysis focuses on the JOBS II eligibility trial that was implemented to test the effectiveness of a job search seminar in decreasing the negative mental health effects commonly associated with job loss. We provide a comparative analysis of the data from the two approaches with prior distributions that are both reasonable in the context of the data and comparable across the model specifications. We show that the approaches can lead to different evaluations of the treatment.