I discuss predicting outcomes and the roles of causation and sampling design.

This article presents a counterintuitive result regarding the estimation of a regression slope coefficient. Paradoxically, the precision of the slope estimator can deteriorate when additional information is used to estimate its value. In a randomized experiment, the distribution of baseline...

The general Gauss–Markov model, Y = Xβ + e, E(e) = 0, Cov(e) = σ <Superscript>2</Superscript> V, has been intensively studied and widely used. Most studies consider covariance matrices V that are nonsingular but we focus on the most difficult case wherein C(X), the column space of X, is not contained in C(V)....</superscript>

Penalized regression procedures have become very popular ways to estimate complicated functions. The smoothing spline, for example, is the solution of a minimization problem in a functional space. If such a minimization problem is posed on a reproducing kernel Hilbert space (RKHS), the solution...