Wednesday February 28, 1996, 4:00pm
102 Bradley Hall
Professor Tony Cai
University of Pennsylvania
Novel Wavelet Shrinkage Estimates for Non-equally Spaced Designs
Abstract. The nonparametric regression model has very important applications in statistics as well as many other fields such as signal processing. The Donoho-Johnstone wavelet shrinkage procedures for recovering signals under equally spaced designs have been shown to be near optimal in theory and very useful in practice.
But in many applications, the samples are nonequally spaced. We first show that the direct application of the Donoho-Johnstone procedures to nonequally spaced samples are in many cases suboptimal. We propose a new wavelet shrinkage estimate for nonequally spaced designs. We show that the estimate is near-minimax in global estimation and attains exact minimax rate for pointwise estimation.The procedure is implemented in SPlus. Simulations are conducted and confirm the theoretical results.
The techniques developed can also be applied to linear inverse problems as well as nonparametric hypothesis testing which includes signal detection as a special case. The connections among these problems will also be discussed.
Tea. High tea will be served at 3:30pm in the Lounge.
Emmy's. Certain refreshments will be available at the Emmy's after the talk.