Title: Function Estimation via Asymptotic Equivalence
Abstract:
Recent progress in asymptotic equivalence theory shows that many
nonparametric estimation problems can be approximated by regression with
Gaussian noise (see Brown and Low (1996, AS), Nussbaum (1996, AS),
Grama and Nussbaum (1998, PTRF), etc.). Gaussian regression models allow
relatively simple and straightforward procedures. So a question is posed:
can we convert general nonparametric estimation problems to Gaussian
regression in a constructive way ? In this talk we will discuss a
procedure for that; density estimation will be studied as an example.
Similar procedures work for nongaussian regression, e.g. for
nonparametric generalized linear models and for location type regression
(with heavy tails).
One of the procedures which have been extensively studied in Gaussian
regression is wavelet smoothing. After converting a general
nonparametric estimation problem to regression with Gaussian noise,
we would like to apply a wavelet method. Two new thresholding
procedures will be proposed.
Further topics in asymptotic equivalence theory will be discussed, such as connections to information theory, and infinitely divisible approximations. The talk is based on joint work with L.D. Brown, T.T. Cai, J.T. G. Hwang, M.G. Low, M. Nussbaum, et al.
Seminar to be held in Room 107, 24 Hillhouse at 4:15 pm