We show that the Wald statistic still identifies a causal effect if instrument monotonicity is replaced by a weaker condition, which states that the potential propensities to be treated with or without the instrument should have the same distribution, conditional on potential outcomes. This...

We present elementary proofs to some formulas given without proofs by K. A. West and J. McClellan in 1993, B. L. Evans and J. H. McClellan in 1994, and J. Cavicchi in 2002, for the calculation of the convolution integrals and sums of piecewise defined functions. Unlike “divide and conquer”...

In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently it has been shown that they can also be exploited in species sampling...