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Joint Statistics / Biostatistics and Medical Informatics Seminar

Inference with Balls and Envelopes

Christopher Genovese, PhD,
Department of Statistics, Carnegie Mellon University

Wednesday, March 3, 2004, 4-5 p.m.

1221 Computer Sciences and Statistics building, 1210 West Dayton St.

ABSTRACT

In this talk, I will discuss recent work on constructing confidence balls for an unknown function in nonparametric regression problems. The goal is to construct confidence balls in a specified metric with (asymptotically) uniform coverage that can then be constrained by available side information. I'll describe two approaches. The first extends results by Beran and Dumbgen (1998) to wavelet bases and weighted L2 loss. The second, still in progress, constructs L^\infty confidence balls -- confidence bands -- that account for bias in a truncated basis expansion. Our approach follows Baraud (2002) in using a family of tests to select subspaces on which to construct the balls. I will demonstrate these methods through an analysis of the Cosmic Microwave Background spectrum, which is used by cosmologists to understand the physics of the early universe.

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