It is well known that it is difficult to construct minimax optimal designs. Furthermore, since in practice we never know the true error variance, it is important to allow small deviations and construct robust optimal designs. We investigate a class of minimax optimal regression designs for models with heteroscedastic errors that are robust against possible misspecification of the error variance. Commonly used A‐, c‐, and I‐optimality criteria are included in this class of minimax optimal designs. Several theoretical results are obtained, including a necessary condition and a reflection symmetry for these minimax optimal designs. In this article, we focus mainly on linear models and assume that an approximate error variance function is available. However, we also briefly discuss how the methodology works for nonlinear models. We then propose an effective algorithm to solve challenging nonconvex optimization problems to find minimax designs on discrete design spaces. Examples are given to illustrate minimax optimal designs and their properties.

In theory, the probabilistic linkage method provides two distinct advantages over nonprobabilistic methods, including minimal rates of linkage error and accurate measures of these rates for data users. However, implementations can fall short of these expectations either because the conditional independence assumption is made, or because a model with interactions is used but lacks the identification property. In official statistics, this is currently the main challenge to the automated production and use of linked data. To address this challenge, a new methodology is described for proper linkage problems, where matched records may be identified with a probability that is bounded away from zero, regardless of the population size. It models the number of neighbours of a given record, i.e. the number of resembling records. To be specific, the proposed model is a finite mixture where each component is the sum of a Bernoulli variable with an independent Poisson variable. It has the identification property and yields solutions for many longstanding problems, including the evaluation of blocking criteria and the estimation of linkage errors for probabilistic or nonprobabilistic linkages, all without clerical reviews or conditional independence assumptions. Thus it also enables unsupervised machine learning solutions for record linkage problems.