Department of Statistics Seminar
North Carolina State University

presents

Dr. Xiao-li Meng

Harvard University

Self-Consistency and Wavelet Shrinkage With Irregular Designs

ABSTRACT

Wavelet shrinkage is a powerful curve and surface fitting method which has attracted enormous attention from researchers across different fields, including applied mathematicians, computer scientists, engineers, and statisticians. Wavelet estimators enjoy excellent theoretical properties and they are capable of adapting to very complex spatial and frequency inhomogeneities. However, standard wavelet methods are not directly applicable in many statistical applications (e.g., non-parametric regressions) because the regression design points are typically not equispaced, as required by the fast wavelet algorithms. The current most common approach is to transform an irregular-design problem into a regular one via interpolation. Although such interpolation-based methods are effective for various applications, they typically do not retain the full information available in the observed data for wavelet regressions.

Self-consistency is a fundamental statistical invariance principle for constructing the most efficient statistical estimators in many incomplete data problems. By viewing an irregular design as an incomplete regular design, we can obtain self-consistent wavelet estimators with arbitrary designs, without the need of making the (implicit) smoothness assumptions underlying interpolation-based methods. Simulation results strongly support the expectation that the self-consistent approach better utilizes the information available in the observed data. When a smoothness assumption is appropriate, it can easily be incorporated into the self-consistent approach directly to produce an estimator that is more efficient than either the pure self-consistent estimator and the pure interpolation-based estimator.

The talk explains general ideas, describes some specific algorithms, presents empirical evidence, and ends with a beautiful punch line--or rather--a beautiful picture!

This is joint work with Thomas Lee of Colorado State University.

Friday, March 21, 2003

3:35 - 4:35 pm

206 Cox Hall

Refreshments will be served on the second floor of Dabney Hall (left of Room 222) at 3:00 pm.