Designs for estimating the difference between two responses

In this paper the problem of designing experiments for estimating the difference between responses at two arbitrary points in the region of interest is considered. Under the average mean squared error criterion the design moment conditions have been worked out. The results have been applied to the class of central composite designs.     

Construction of minimum aberration blocked two-level regular factorial designs

ABSTRACT

In this article, we consider the construction of minimum aberration 2^{n ? k}: 2^p designs with respect to some existing combined wordlength patterns, where a 2^{n ? k}: 2^p design is a blocked two-level design with n treatment factors, 2^p blocks, and N = 2^q runs with q = n ? k. Two methods are proposed for two situations: n ? 2^{q ? p} ? 1 and n > N/2. These methods enable us to obtain some new minimum aberration 2^{n ? k}: 2^p designs from existing minimum aberration unblocked and blocked designs. Examples are included to illustrate the theory.     

The elasticity of labor demand and the minimum wage

We show that, contrary to widespread belief, low-pay workers do not generally prefer that the minimum wage rate be increased until the labor demand is unitary elastic. Rather, there exists a critical value of elasticity of labor demand so that increases in the minimum wage rate make low-pay workers better off for higher elasticities, but worse off for lower elasticities. This critical value decreases with unemployment benefits and increases with workers’ risk aversion. We also show that in some countries the benefits for long-term unemployed are so low that workers would probably prefer that the minimum wage rate be decreased. I thank the anonymous referees for helpful suggestions.     

A simple method to obtain minimum aberration split-plot designs

ABSTRACT

Split-plot designs have been utilized in factorial experiments with some factors applied to larger units and others to smaller units. Such designs with low aberration are preferred when the experimental size and the number of factors considered in both whole plot and subplot are determined. The minimum aberration split-plot designs can be obtained using either computer algorithms or the exhausted search. In this article, we propose a simple, easy-to-operate approach by using two ordered sequences of columns from two orthogonal arrays in obtaining minimum aberration split-plot designs for experiments of sizes 16 and 32.     

Calculating the mvue of the fraction nonconforming for the bivariate normal

The minimum variance unbiased estimator of the proportion lying outside an m-dimensional rectangle for multivariate normal populations was derived by Baillie (1987a, b). The estimator is a natural extension of a univariate estimator widely used in acceptance sampling. Computation of the multivariate estimator is nontrivial; one must integrate a multivariate density over the intersection of an m-dimensional ellipsoid and an m-dimensional rectangle. We propose an algorithm for the bivariate case which involves a one-dimensional numerical integration and calls to routines for either an incomplete beta function or a Student's t cumulative distribution function     

On the Use of Semi-folding in Regular Blocked Two-level Factorial Designs

In this article, we consider experimental situations where a blocked regular two-level fractional factorial initial design is used. We investigate the use of the semi-fold technique as a follow-up strategy for de-aliasing effects that are confounded in the initial design as well as an alternative method for constructing blocked fractional factorial designs. A construction method is suggested based on the full foldover technique and sufficient conditions are obtained when the semi-fold yields as many estimable effects as the full foldover.     

Unbiastld estimation of parametric functions in sampling from two two-truncation parameter families

We consider the problem of UMVU estimation of a U-estimable function of four unknown truncation parameters based on two independent random samples from two two-truncation parameter families. In particular, we obtain the UMVU estimator of functional, P (Y > X). Also the confidence intervals for some parametric functions are obtained.     

Resource smoothing: A cost minimization approach

From the available literature, there seems to be no defined approach to resource smoothing exercise except those attempted by Weist (1967, Management Science, 13, B359-B377) and Burgess and Killebrew (1962, Journal of Industrial Engineering, 13, 76-83). The aim of the smoothing exercise is to achieve optimal resource usage by avoiding high peaks and deep valleys in the project resource profile. The general approach has always been to move some activities with floats in the high peak regions to be started at a later date, and as this is done, the valleys will be filled to smooth the resource profile subject of course to time constraint. If this approach is followed as it is, it would be difficult to determine optimality especially when many resources are involved. A cost minimization approach is envisaged in the present study with no limitation on the number of resource inputs. In a situation where the resources are assumed to have the same value, the cost assigned to each of them should be similar. The method follows the general concept but with a difference; cost of the activity in question is considered. The exercise is continued until all the floats are exhausted. The optimum result would then be the one with the minimum cost profile. From examples used for the evaluation, the results obtained are comparable to those of the above two researchers, and some with better results in the majority of cases.     

A characteristic function approach to the biased sampling model,with application to robust logistic regression

Many sampling problems from multiple populations can be considered under the semiparametric framework of the biased, or weighted, sampling model. Included under this framework is logistic regression under case–control sampling. For any model, atypical observations can greatly influence the maximum likelihood estimate of the parameters. Several robust alternatives have been proposed for the special case of logistic regression. However, some current techniques can exhibit poor behavior in many common situations. In this paper a new family of procedures are constructed to estimate the parameters in the semiparametric biased sampling model. The procedures incorporate a minimum distance approach, but are instead based on characteristic functions. The estimators can also be represented as the minimizers of quadratic forms in simple residuals, thus yielding straightforward computation. For the case of logistic regression, the resulting estimators are shown to be competitive with the existing robust approaches in terms of both robustness and efficiency, while maintaining affine equivariance. The approach is developed under the case–control sampling scheme, yet is shown to be applicable under prospective sampling logistic regression as well.