Title
Function Estimation via Asymptotic Equivalence
Speaker
Harrison Zhou, Cornell University
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.
