Quasi-universal bandwidth selection for kernel density estimators

Let (f) over cap(n), h denote the kernel density estimate based on a sample of size n drawn from an unknown density f. Using techniques from L-2 projection density estimators, the author shows how to construct a data-driven estimator (f) over cap(n), (H) which satisfies (sup)(bounded) lim sup(n --> infinity) integral E\(f) over cap(n),(H)(x) - f(x)\(2)dx/inf(h > 0)integral E\(f) over cap(n,h)(x)(\)(2)dx = 1. This paper is inspired by work of Stone (1984), Devroye and Lugosi (1996) and BirgC and Massart (1997).