## Andrew Carter, Yale University

### Asymptotic Equivalence of Nonparametric Experiments

The Le Cam
deficiency distance between statistical experiments can be
characterized by how closely one set of distributions can be
approximated by a randomization applied to the other set of
distributions. Recently, Brown and Low (1996) and Nussbaum (1996) have
established Gaussian approximations to nonparametric regression and
density estimation experiments, respectively, in terms, of this
distance. This talk will discuss some new general techniques for
bounding the deficiency. A simple example of a normal approximation to
a binomial will be used to demonstrate the bounds. There are two
techniques which work under different conditions on the parameter set:
one relies on classical local-limit theories to bound the distance and
the other takes advantage of a coupling between symmetric
distributions. These bounds between binomial and normal experiments
are the key pieces in constructing an approximation between the
density estimation experiment and a Gaussian process.