Towards Completely-Drive-Driven Functional Estimation

Time: 10:00 am, 07/07/2011
Lecture Room: SEIEE Building 5-406
Speaker: Huo Xiaoming
Topic: Towards Completely-Drive-Driven Functional Estimation 

Suppose input variable Xi and response yi have the relation: yi = f(Xi) +
i, where i are i.i.d. noises. Furthermore, we assume that Xi’s are ‘adequately’ sampled within a domain Ω and function f(·) is unknown. Estimating f(·) is called functional estimation, and is the objective for many well-known parametric and nonparametric methods. The most influential existing approach follows the following framework: (1) assume that f belongs to a predetermined functional class F; (2) Derive analytic description of the basis function of F in Ω; (3) Turn the functional estimation problem into a quadratic programming problem, for which analytical and numerical solutions are available. This approach runs into difficulty when the domain Ω is irregular, or nonstandard.
We have developed a strategy that can circumvent this difficulty. In particular, a method that is completely driven by data is invented to solve the functional estimation problem. We show that nearly all good asymptotic properties of the existing state-of-the-art approaches are inherited by our data-driven approach. These properties include optimal rate of convergence, asymptotic optimality, etc. We use numerical examples to demonstrate better performance of the proposed method when the domain Ω is irregular. This is a joint work with Zhouwang Yang and Huizhi Xie.

[ 2011-07-07 ]