Explore the vast range of titles available.

We consider the effective sample size, based on Godambe information, for block likelihood inference which is an attractive and computationally feasible alternative to full likelihood inference for large correlated datasets. With reference to a Gaussian random field having a constant mean, we explore how the choice of blocks impacts this effective sample size. This is done by introducing a column-wise blocking method which spreads out the spatial points within each block, instead of keeping them close together as the existing row-wise blocking method does. It is seen that column-wise blocking can lead to considerable gains in effective sample size and efficiency compared to row-wise blocking, while retaining computational simplicity. Analytical results in this direction are obtained under the AR (1) model. The insights so found facilitate the study of other one-dimensional correlation models as well as correlation models on a plane, where closed form expressions are intractable. Simulations are seen to provide support to our conclusions.

With reference to a baseline parametrization, we explore highly efficient, fractional factorial designs for inference on the main effects and, perhaps, some interactions. Our tools include approximate theory together with certain, carefully devised discretization procedures. The robustness of these designs to possible model misspecification is investigated using a minimaxity approach. Examples are given to demonstrate that our technique works well even when the run size is quite small.

Split-plot designs find wide applicability in multifactor experiments with randomization restrictions. Practical considerations often warrant the use of unbalanced designs. This study investigates randomization-based causal inference in split-plot designs that are possibly unbalanced. An extension of the balanced case yields an expression for the sampling variance of a treatment contrast estimator, as well as a conservative estimator of the sampling variance. However, the bias of this variance estimator does not vanish, even when the treatment effects are strictly additive. A careful and involved matrix analysis is employed to overcome this difficulty, resulting in a new variance estimator that becomes unbiased under milder conditions. We propose a construction procedure that generates such an estimator with a minimax bias. Empirical studies suggest the superiority of the proposed estimator with respect to bias uniformly across different populations. Furthermore, this superiority does not come at the cost of a large inflation of the mean squared error.

This article considers causal inference for treatment contrasts from a randomized experiment using potential outcomes in a finite population setting. Adopting a Neymanian repeated sampling approach that integrates such causal inference with finite population survey sampling, an inferential framework is developed for general mechanisms of assigning experimental units to multiple treatments. This framework extends classical methods by allowing the possibility of randomization restrictions and unequal replications. Novel conditions that are \"milder\" than strict additivity of treatment effects, yet permit unbiased estimation of the finite population sampling variance of any treatment contrast estimator, are derived. The consequences of departures from such conditions are also studied under the criterion of minimax bias, and a new justification for using the Neymanian conservative sampling variance estimator in experiments is provided. The proposed approach can readily be extended to the case of treatments with a general factorial structure.

In an order-of-addition experiment, each treatment is a permutation of m components. It is often unaffordable to test all the m! possible treatments, and thus the design problem arises. We consider a flexible model that incorporates the order of each pair of components and can also account for the distance between the two components in every such pair. Under this model, the optimality of the uniform design measure is established, via the approximate theory, for a broad range of criteria. Coupled with an eigenanalysis, this result serves as a benchmark that paves the way for assessing the efficiency and robustness of any exact design. The closed-form construction of a class of robust optimal fractional designs that can also facilitate model selection is explored and illustrated.

We consider two-level fractional factorial designs under a baseline parametrization that arises naturally when each factor has a control or baseline level. While the criterion of minimum aberration can be formulated as usual on the basis of the bias that interactions can cause in the estimation of main effects, its study is hindered by the fact that level permutation of any factor can impact such bias. This poses a serious challenge especially in the practically important highly fractionated situations where the number of factors is large. We address this problem for regular designs via explicit consideration of the principal fraction and its cosets, and obtain certain rank conditions which, in conjunction with the idea of minimum moment aberration, are seen to work well. The role of simple recursive sets is also examined with a view to achieving further simplification. Details on highly fractionated minimum aberration designs having up to 256 runs are provided.

Under the potential outcomes framework, we propose a randomization based estimation procedure for causal inference from split-plot designs, with special emphasis on 2² designs that naturally arise in many social, behavioral and biomedical experiments. Point estimators of factorial effects are obtained and their sampling variances are derived in closed form as linear combinations of the between- and within-group covariances of the potential outcomes. Results are compared to those under complete randomization as measures of design efficiency. Conservative estimators of these sampling variances are proposed. Connection of the randomization-based approach to inference based on the linear mixed effects model is explored. Results on sampling variances of point estimators and their estimators are extended to general split-plot designs. The superiority over existing model-based alternatives in frequency coverage properties is reported under a variety of simulation settings for both binary and continuous outcomes.

Quaternary code (QC) designs form an attractive class of nonregular factorial fractions. We develop a complementary set theory for characterizing optimal QC designs that are highly fractionated in the sense of accommodating a large number of factors. This is in contrast to existing theoretical results which work only for a relatively small number of factors. While the use of imaginary numbers to represent the Gray map associated with QC designs facilitates the derivation, establishing a link with foldovers of regular fractions helps in presenting our results in a neat form.

With reference to regular fractions of general s-level factorials, we consider the design criterion of general minimum lower order confounding (GMC) that aims, in an elaborate manner, at keeping the lower order factorial effects unaliased with one another to the extent possible. Using a finite projective geometric formulation, this involves identification of the alias sets with the points of the geometry; we derive explicit formulae connecting the key terms for this criterion with the complementary set. These results are then applied to find optimal designs under the GMC criterion.

We consider regular fractions of s-level factorials arranged in block designs. Optimal designs are explored under the criterion of general minimum lower order confounding which aims, in an elaborate manner, at keeping the lower order factorial effects unaliased with one another and unconfounded with blocks. A finite projective geometric formulation, that identifies the alias sets with the points and the blocking system with a flat of the geometry, forms the mathematical basis of our approach. Theoretical results and tables are obtained in terms of complementary sets and an idea of double complementation is found to be useful in some situations.