A new class of specification tests for stochastic differential equations (SDE) is proposed to determine whether the probability integral transform estimated model generates an independent and identically distributed uniform random variable. The are based on Neyman’s smooth test, appropriately adjusted correct both size distortion arising from having estimate unknown parameters SDE possible depe...

With elementary means, we prove a stronger run time guarantee for the univariate marginal distribution algorithm (UMDA) optimizing LeadingOnes benchmark function in desirable regime with low genetic drift. If population size is at least quasilinear, then, high probability, UMDA samples optimum number of iterations that linear problem divided by logarithm UMDA's selection rate. This improves ove...