Balanced Asymmetrical Nearly Orthogonal Designs for first and second order effect estimation

A method for constructing asymmetrical (mixed-level) designs, satisfying the balancing and interaction estimability requirements with a number of runs as small as possible, is proposed in this paper. The method, based on a heuristic procedure, uses a new optimality criterion formulated here. The proposed method demonstrates efficiency in terms of searching time and optimality of the attained designs. A complete collection of such asymmetrical designs with two- and three-level factors is available. A technological application is also presented.     

αn–Designs

This paper defines a broad class of resolvable incomplete block designs called α_n–designs, of which the original α–designs are a special case with n = 1. The statistical and mathematical properties of α–designs extend naturally to these n –dimensional designs. They are a flexible class of resolvable designs appropriate for use in factorial experiments, in constructing efficient t –latinized resolvable block designs, and for enhancing the existing class of α–designs for a single treatment factor.     

A method for constructing supersaturated designs and its Es2 optimality

A lower bound for the Es² value of an arbitrary supersaturated design is derived. A general method for constructing supersaturated designs is proposed and shown to produce designs with n runs and m = k(n — 1) factors that achieve the lower bound for Es² and are thus optimal with respect to the Es² criterion. Within the class of designs given by the construction method, further discrimination can be made by minimizing the pairwise correlations and using the generalized D and A criteria proposed by Wu (1993). Efficient designs of 12, 16, 20 and 24 runs are constructed by following this approach.     

Andrews plots for multivariate data: some new suggestions and applications

Andrews plots (Biometrics 28 (1972) 125-136), as a tool to graphically interpret multivariate data, have recently gained considerable recognition. In this article, we first review the previous literature and then suggest a modification to the traditional Andrews plots. Finally, we illustrate a few new applications of these plots in robust design studies and in correspondence analysis, using real data.     

EFFICIENT BLOCK DESIGNS FOR CORRELATED OBSERVATIONS

Current methods for the design of efficient incomplete block experiments when the observations within a block are dependent usually involve computer searches of binary designs. These searches give little insight into the features that lead to efficiency, and can miss more efficient designs. This paper aims to develop some approximations which give some insight into the features of a design that lead to high efficiency under a generalized least-squares analysis for a known dependence structure, and to show that non-binary designs can be more efficient for some dependence structures. In particular, we show how neighbour balance and end plot balance are related to the design efficiency for low-order autoregressions, and that under moderate positive dependence, replication at lag two can sometimes increase efficiency.     

Designs for approximately linear regression: Maximizing the minimum coverage probability of confidence ellipsoids

The classical D-optimality principle in regression design may be motivated by a desire to maximize the coverage probability of a fixed-volume confidence ellipsoid on the regression parameters. When the fitted model is exactly correct, this amounts to minimizing the determinant of the covariance matrix of the estimators. We consider an analogue of this problem, under the approximately linear model E[y|x] = θ^Tz(x) + f(x). The nonlinear disturbance f(x) is essentially unknown, and the experimenter fits only to the linear part of the response. The resulting bias affects the coverage probability of the confidence ellipsoid on θ. We study the construction of designs which maximize the minimum coverage probability as f varies over a certain class. Explicit designs are given in the case that the fitted response surface is a plane.     

Book Reviews

Books reviewed:
Bosq, D. Nonparametric Statistics for Stochastic Processes: Estimation and Prediction
Khuri, A.I., Mathew, T. & Sinha, B.K. Statistical Tests for Mixed Linear Models
Latouche, G. & Ramaswami, V. Introduction to Matrix Analytic Methods in Stochastic Modeling
Maitra, A.P. & Sudderth, W.D. Discrete Gambling and Stochastic Games
Rolski, T., Schmidli, H., Schmidt, V. & Teugels, J. Stochastic Processes for Insurance and Finance
Chung, K.L. & Williams, R.J. Introduction to Stochastic Integration     

Influential observations in view of design and inference

In this paper we consider the measures for detecting the influential observations w.r.t. one or several parameters of interest at the design stage. We also consider the Cook's measure for detecting the influential observations at the inference stage. We study the interrelationship between two kinds of measures.     

Designing completely randomized experiments to detect ordered treatment effects: an empirical study

In designing experiments the researcher frequently must decide as to how to allocate fixed resources among k factor levels (Cox (1958)). This study investigates the effects on the power of a test caused by changes in: the sample size (n); the number of factor levels (k); the allocation of fixed total observations (N) among k and n: the shift parameter (ø); the type of parent population sampled; and, the type of ordered location alternative involved. Using Monte Carlo methods the powers of eight test procedures specifically devised to detect ordered treatment effects under completely randomized designs were evaluated along with those of the more general one-way F test. The results are of interest to researchers in all fields of application.     

D-Optimal Designs for Covariate Parameters in Block Design Set Up

The problem considered is that of finding D-optimal design for the estimation of covariate parameters and the treatment and block contrasts in a block design set up in the presence of non stochastic controllable covariates, when N = 2(mod 4), N being the total number of observations. It is clear that when N ≠ 0 (mod 4), it is not possible to find designs attaining minimum variance for the estimated covariate parameters. Conditions for D-optimum designs for the estimation of covariate parameters were established when each of the covariates belongs to the interval [?1, 1]. Some constructions of D-optimal design have been provided for symmetric balanced incomplete block design (SBIBD) with parameters b = v, r = k = v ? 1, λ =v ? 2 when k = 2 (mod 4) and b is an odd integer.