On best affine prediction

The theory of best affine prediction (BAP) is extended to the vector case with possibly singular variance matrix of the predictor variable. The theory is then applied to derive Thomson’s classical predictor for factor scores, allowing for a singular variance matrix of the factors. The results are formulated in a free distribution setting. Further, Bartlett’s estimator is considered and compared with Thomson’s predictor. The authors are thankful to the two referees, one for a suggestion that led to the Addendum of the paper, and the other one for several very useful remarks. Research supported by the Spanish grant BEC2000-0983.     

The TOWS matrix—A tool for situational analysis

This article has two main purposes. One is to review general considerations in strategic planning and the second to introduce the TOWS Matrix for matching the environmental threats and opportunities with the company's weaknesses and especially its strengths. These factors per se are not new; what is new is systematically identifying relationships between these factors and basing strategies on them. There is little doubt that strategic planning will gain greater prominence in the future. Any organization—whether military, product-oriented, service-oriented or even governmental—to remain effective, must use a rational approach toward anticipating, responding to and even altering the future environment.     

Adaptation of Tastes to Constraints

This paper examines a model in which people’s preferences adjust to changes in their relative ability to attain various goals. Preference changes are modeled as changes in the configuration of weights (or values) attached to these goals. The model permits to explain common prototype changes of preferences such as the ‘sour grapes’ or the ‘overcompensating’ phenomenon. It is found that whether the first or the second phenomenon occurs depends on whether a goal is easy or difficult to substitute by other goals. If two goals are sufficiently strong substitutes for each other, no weight will be placed on that goal which is harder to attain. The results readily apply to the standard microeconomic set-up involving goods and prices, rather than abstract goals and abilities. In this case, one implication of the model is that only a subset of the overall commodity space is relevant for everyday consumer choice, which reduces the complexity of the choice procedure. The model also permits to explain how new and unfamiliar products are incorporated into the consumer’s preference pattern.     

Optimal paired comparison designs for first-order interactions

In many fields of applications paired comparisons are used in which either full or partial profiles of the alternatives are presented. For this situation we introduce an appropriate model and derive optimal designs in the presence of interactions when all attributes have the same number of levels.     

Best quadratic and positive semidefinite unbiased estimation of the variance matrix of the multivariate normal distribution

A BQPUE (best quadratic and positive semidefinite unbiased estimator) of the matrix V for the distribution vec X^′∽N_np(vec M^′, U?V) is being given. It is unique, although still depending on U and M. When U = I and M = (μ,…,μ), we get a well-known (unique) result not depending on M.