Saturated locally optimal designs under differentiable optimality criteria

We develop general theory for finding locally optimal designs in a class of single-covariate models under any differentiable optimality criterion. Yang and Stufken [Ann. Statist. 40 (2012) 1665-1681] and Dette and Schorning [Ann. Statist. 41 (2013) 1260-1267] gave complete class results for optimal designs under such models. Based on their results, saturated optimal designs exist; however, how to find such designs has not been addressed. We develop tools to find saturated optimal designs, and also prove their uniqueness under mild conditions.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1263 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Cram\'{e}r-type large deviations for samples from a finite population

Cram\'{e}r-type large deviations for means of samples from a finite population are established under weak conditions. The results are comparable to results for the so-called self-normalized large deviation for independent random variables. Cram\'{e}r-type large deviations for the finite population Student $t$-statistic are also investigated.Comment: Published at http://dx.doi.org/10.1214/009053606000001343 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Efficient solutions of self-consistent mean field equations for dewetting and electrostatics in nonuniform liquids

We use a new configuration-based version of linear response theory to efficiently solve self-consistent mean field equations relating an effective single particle potential to the induced density. The versatility and accuracy of the method is illustrated by applications to dewetting of a hard sphere solute in a Lennard-Jones fluid, the interplay between local hydrogen bond structure and electrostatics for water confined between two hydrophobic walls, and to ion pairing in ionic solutions. Simulation time has been reduced by more than an order of magnitude over previous methods.Comment: Supplementary material included at end of main pape