Asymptotic Inference for Optimal Rerandomization Designs

Recently a computational-based experimental design strategy called rerandomization has been proposed as an alternative or complement to traditional blocked designs. The idea of rerandomization is to remove, from consideration, those allocations with large imbalances in observed covariates according to a balance criterion, and then randomize within the set of acceptable allocations. Based on the Mahalanobis distance criterion for balancing the covariates, we show that asymptotic inference to the population, from which the units in the sample are randomly drawn, is possible using only the set of best, or ‘optimal’, allocations. Finally, we show that for the optimal and near optimal designs, the quite complex asymptotic sampling distribution derived by Li et al. (2018), is well approximated by a normal distribution.

A Fast and Robust Way to Estimate Overlap of Niches, and Draw Inference

The problem of quantifying the overlap of Hutchinsonian niches has received much attention lately, in particular in quantitative ecology, from where it also originates. However, the niche concept has the potential to also be useful in many other application areas, as for example in economics. We are presenting a fully nonparametric, robust solution to this problem, along with exact shortcut formulas based on rank-statistics, and with a rather intuitive probabilistic interpretation. Furthermore, by deriving the asymptotic sampling distribution of the estimators, we are proposing the first asymptotically valid inference method, providing confidence intervals for the niche overlap. The theoretical considerations are supplemented by simulation studies and a real data example.

Failure Probability Estimation Using Asymptotic Sampling and Its Dependence upon the Selected Sampling Scheme

The article examines the use of Asymptotic Sampling (AS) for the estimation of failure probability. The AS algorithm requires samples of multidimensional Gaussian random vectors, which may be obtained by many alternative means that influence the performance of the AS method. Several reliability problems (test functions) have been selected in order to test AS with various sampling schemes: (i) Monte Carlo designs; (ii) LHS designs optimized using the Periodic Audze-Eglājs (PAE) criterion; (iii) designs prepared using Sobol’ sequences. All results are compared with the exact failure probability value.