Optimal and efficient designs for Gompertz regression models

Gompertz functions have been widely used in characterizing biological growth curves. In this paper we consider D-optimal designs for Gompertz regression models. For homoscedastic Gompertz regression models with two or three parameters, we prove that D-optimal designs are minimally supported. Considering that minimally supported designs might not be applicable in practice, alternative designs are proposed. Using the D-optimal designs as benchmark designs, these alternative designs are found to be efficient in general.     

A constructive aisle design model for unit-load warehouses with multiple pickup and deposit points

We develop a network-based warehouse model of individual pallet locations and their interactions with appropriate cross aisles in order to evaluate the expected travel distance of a given design. The model is constructive in that it uses Particle Swarm Optimization to determine the best angles of cross aisles and picking aisles for multiple, pre-determined pickup and deposit (P&D) points in a unit-load warehouse. Our results suggest that alternative designs offer reduced expected travel distance, but at the expense of increased storage space. The opportunity for benefit also seems to decline as P&D points increase in number and dispersion.     

Changes in Students' Science Ability Produced by Multimedia Learning Environments: Application of the Linear Logistic Model for Change

The purpose of this study was to measure changes in students' science proficiency produced by a multimedia learning environment, Astronomy Village: Investigating the Solar System, developed at Wheeling Jesuit University's Center for Educational Technologies with funding from the National Science Foundation. The inquiry‐based design of Astronomy Village supports middle school students in learning fundamental concepts in life, earth, and physical science. Astronomy Village was compared to an alternative treatment that simulated elements of traditional science instruction using web site access to background materials and content in Astronomy Village. The results indicate sizable treatment effects for two groups of Astronomy Village students, as well as for the alternative treatment group. Differences in the treatment effect sizes among the three treatment groups reveal the relative merits of different approaches to using technology. The Linear Logistic Model for Change applied in this study is beneficial for comparing alternative uses of technology, since it separates effects due to treatments from natural trend effects and eliminates drawbacks of traditional statistical designs for pretest‐posttest changes.     

Virtually balanced incomplete block designs for v = 22, k = 8, and λ = 4

When basic necessary conditions for the existence of a balanced incomplete block design are satisfied, the design may still not exist or it may not be known whether it exists. In either case, other designs may be considered for the same parameters. In this article we introduce a class of alternative designs, which we will call virtually balanced incomplete block designs. From a statistical point of view these designs provide efficient alternatives to balanced incomplete block designs, and from a combinatorial point of view they offer challenging new questions. © 1995 John Wiley & Sons, Inc.     

The classification of doubly transitive affine designs

We classify the doubly transitive affine designs. The proof uses the classification of the multiply transitive permutation groups.     

The number of feasible designs in a compatibility matrix

Many design and planning problems consist of a number of distinct subsystems. Generally, there are several possible alternatives for design of a subsystem. However, an alternative for one subsystem may be incompatible with an alternative for another subsystem. Thus, a feasible design is one that incorporates one alternative for each subsystem such that no pairwise incompatibilities exist. Several such design and planning problems have been formulated as compatibility matrices. The feasible designs can be identified by using an efficient algorithm. This paper shows that, in general, the exact number of feasible designs decreases exponentially with the increase in the number of incompatible pairs. This finding should motivate more potential users to employ the compatibility matrix approach.     

New imputation methods for missing data using quantiles

The problem of missing values commonly arises in data sets, and imputation is usually employed to compensate for non-response. We propose a novel imputation method based on quantiles, which can be implemented with or without the presence of auxiliary information. The proposed method is extended to unequal sampling designs and non-uniform response mechanisms. Iterative algorithms to compute the proposed imputation methods are presented. Monte Carlo simulations are conducted to assess the performance of the proposed imputation methods with respect to alternative imputation methods. Simulation results indicate that the proposed methods perform competitively in terms of relative bias and relative root mean square error.     

Option and forward contracting with asymmetric information: Valuation issues in supply chains

We investigate the role of forward commitments and option contracts between a seller (supplier) and a buyer (retailer) in the presence of asymmetric information. In our case, both parties face price and demand uncertainty but the retailer, being closer to the market, has additional information about the true demand and price. The supplier, aware of this asymmetry, and acting as a Stackelberg leader, designs a contracting arrangement that best meet his interest. We contrast the role of forward and option contracts in this environment and identify cases where combinations of the two are dominant. Finally, we investigate how alternative contracting arrangements alter the expected value of obtaining information that eliminates asymmetric information.     

A numerical study of designs for sporting contests

Operational Research may be used to compare different designs for a sporting contest or tournament. This paper considers a methodology for this purpose. We propose a number of tournament metrics that can be used to measure the success of a sporting contest or tournament, and describe how these metrics may be evaluated for a particular tournament design. Knowledge of these measures can then be used to compare competing designs, such as round-robin, pure knockout and hybrids of these designs. We show, for example, how the design of the tournament influences the outcome uncertainty of the tournament and the number of unimportant matches within the tournament. In this way, where new designs are proposed, the implications of these designs may be explored within a modelling paradigm. In football (soccer), the UEFA Champions League has adopted a number of designs over its 50 year history; the design of the tournament has been modified principally in response to the changing demands of national league football and television – the paper uses this particular tournament to illustrate the methodology.     

Optimal designs for estimating the coefficients of the lower frequencies in trigonometric regression models

In the common Fourier regression model we determine the optimal designs for estimating the coefficients corresponding to the lower frequencies. An analytical solution is provided which is found by an alternative characterization of c-optimal designs. Several examples are provided and the performance of the D-optimal design with respect to the estimation of the lower order coefficients is investigated. The results give a complete answer to an open question which was recently raised in the literature.     

Modelling undesirable outputs with zero sum gains data envelopment analysis models

Data envelopment analysis (DEA) literature has proposed alternative models for performance assessment in the presence of undesirable outputs, such as pollutant emissions, where increased outputs imply reduced performance. However, the case where global equilibrium of outputs should be imposed has not yet been considered. We propose that the zero sum gains DEA (ZSG-DEA) models look especially suitable for treating equilibrium models, where the sum of the quantities produced by all decision-making units can be set as the upper admissible bound. This paper uses ZSG-DEA models to evaluate the carbon dioxide emission case study, which can be considered part of the Kyoto Protocol statement.     

Concerning Difference Matrices

Several new constructions for difference matrices are given. One classof constructions uses pairwise balanced designs to develop newdifference matrices over the additive group of GF (q). A second class of constructions gives difference matrices overgroups whose orders are not (necessarily) prime powers.     

Construction of sliced (nearly) orthogonal Latin hypercube designs

Sliced Latin hypercube designs are very useful for running a computer model in batches, ensembles of multiple computer models, computer experiments with qualitative and quantitative factors, cross-validation and data pooling. However, the presence of highly correlated columns makes the data analysis intractable. In this paper, a construction method for sliced (nearly) orthogonal Latin hypercube designs is developed. The resulting designs have flexible sizes and most are new. With the orthogonality or near orthogonality being guaranteed, the space-filling property of the resulting designs is also improved. Examples are provided for illustrating the proposed method.     

Analysis of means approach in advanced designs

Analysis of means (ANOM), similar to Shewhart control chart that exhibits individual mean effects on a graphical display, is an attractive alternative mean testing procedure for the analysis of variance (ANOVA). The procedure is primarily used to analyze experimental data from designs with only fixed effects. Recently introduced, the ANOM procedure based on the q‐distribution (ANOMQ procedure) generalizes the ANOM approach to random effects models. This article reveals that the application of ANOM and ANOMQ procedures in advanced designs such as hierarchically nested and split‐plot designs with fixed, random, and mixed effects enhances the data visualization aspect in graphical testing. Data from two real‐world experiments are used to illustrate the proposed procedure; furthermore, these experiments exhibit the ANOM procedures' visualization ability compared with ANOVA from the point of view of the practitioner.     

The Mantel-Haenszel estimator adapted for complex survey designs is not dually consistent

We show via simulation and counterexamples that the Mantel-Haenszel estimator of a common odds ratio, adapted for complex survey designs using survey weights, is inconsistent for sparse-data limiting models. We also propose an alternative estimator that is consistent for sparse-data limiting models satisfying a positivity condition, but not for large-strata limiting models.     

Mathematical Modeling of Multilayer Filters for Telecommunication

The article presents an interactive approach to the design of Wavelength Division Multiplexing (WDM) filters that combines classical design methods for multi-resonator systems with a semi-heuristic integer optimization method. This approach proves to be exceptionally efficient from the computational point of view and generates a whole range of different filter designs with virtually equivalent spectral properties. The article also considers a method for analyzing the sensitivity of WDM filters to manufacturing errors. The sensitivity analysis relies on computer simulation of thin-layer coating with optical monitoring of layer thickness by the turning point method. This analysis enables the designer to assess alternative filter designs with the purpose of improving manufacturing efficiency.     

Lower bounds and stochastic optimization algorithms for uniform designs with three or four levels

New lower bounds for three- and four-level designs under the centered -discrepancy are provided. We describe necessary conditions for the existence of a uniform design meeting these lower bounds. We consider several modifications of two stochastic optimization algorithms for the problem of finding uniform or close to uniform designs under the centered -discrepancy. Besides the threshold accepting algorithm, we introduce an algorithm named balance-pursuit heuristic. This algorithm uses some combinatorial properties of inner structures required for a uniform design. Using the best specifications of these algorithms we obtain many designs whose discrepancy is lower than those obtained in previous works, as well as many new low-discrepancy designs with fairly large scale. Moreover, some of these designs meet the lower bound, i.e., are uniform designs.

     

Experimental Testing of Advanced Scatter Search Designs for Global Optimization of Multimodal Functions

Scatter search is an evolutionary method that, unlike genetic algorithms, operates on a small set of solutions and makes only limited use of randomization as a proxy for diversification when searching for a globally optimal solution. The scatter search framework is flexible, allowing the development of alternative implementations with varying degrees of sophistication. In this paper, we test the merit of several scatter search designs in the context of global optimization of multimodal functions. We compare these designs among themselves and choose one to compare against a well-known genetic algorithm that has been specifically developed for this class of problems. The testing is performed on a set of benchmark multimodal functions with known global minima.     

Optimal information structure in a simple economic system

In a highly simplified version of a common economic model, the planner can choose among alternative time-varying designs for the information structure in order to steer the system to a target state in an optimal way. The resulting problem is imbedded into a more general one with bilinear dynamics, that is, linear in the control and the state variables but not in both. The existence of a feasible decentralized information structure is studies and designs are found which make the system optimal, given a performance function assigning losses to deviations froma target state. The conditions under which a decentralized structure is optimal are also studied and a numerical case is considered.     

多元分布下单边备择假设的两步检验

x~2检验是熟知的拟合优度检验.它适用于任意的备择假设,尤其是适用于一般的备择假设"H_0不真"的情况.但是,当备择假设是一个单边假设时,x~2检验没有用到单边假设所提供的信息.因此,一个充分利用单边备择假设信息的检验是有可能优于传统的x~2检验的.本文就是利用单边备择假设的信息给出了一个两步检验,并通过一个例子,详细介绍了两步检验法的实施,说明了其应用.