A behind-the-scenes blog about research methods at Pew Research Center. For our latest findings, visit pewresearch.org. Identifying causal relationships from observational data is not easy. Still, ...

Let (X, Y) be a random vector in the plane. We show that a smoothed N.N. estimate of the regression function m(x) = E(Y∣ X = x) is asymptotically normal under conditions much weaker than needed for ...

We define the extension of the so-called 'martingales in the branching random walk' in R or C to some Banach algebras B of infinite dimension and give conditions for their convergence, almost surely ...