Suppose that a random variable X of interest is observed perturbed by independent additive noise Y. This paper concerns the “the least favorable perturbation” Yˆε, which maximizes prediction error E(X−E(X|X+Y))2 in class Y with var(Y)≤ε. We find characterization answer to this question, and show example it can be surprisingly complicated. However, special case where infinitely divisible, soluti...

pedomodels have become a popular topic in soil science and environmentalresearch. they are predictive functions of certain soil properties based on other easily orcheaply measured properties. the common method for fitting pedomodels is to use classicalregression analysis, based on the assumptions of data crispness and deterministic relationsamong variables. in modeling natural systems such as s...