MATH-605. STATISTICS SEMINAR. DEPARTMENT OF MATHEMATICAL SCIENCES.

DATE:	Friday, February 1, 2008. Notice that this is a Friday.
TIME:	4:30-5:30 pm in LN 2205. This talk is given in the Mathematical Sciences Colloquium.
PLACE:	LN 2205.
SPEAKER:	Ou Zhao, University of Michigan.
TITLE:	Isotonic Regression and Stationary Random Walks.

Abstract

This talk consists of two parts, nonparametric estimation of an increasing trend in time series analysis and recent results for stationary random walks (random walks with stationary increments). The estimation is illustrated by global temperature anomalies. These two parts are linked by the use of and focus on stationary processes. In the first part, isotonic estimators are suggested as nonparametric estimators. The asymptotic distribution of estimation error is obtained under nearly minimal conditions. The last value in the series is of particular interest for the temperature anomalies. It is also mathematically challenging, since standard isotonic estimators have to be modified. The derivation of the asymptotic distributions uses some recent advances in central limit theory for stationary random walks. The second part of the talk describes some further development concerning stationary random walks. Techniques centering around martingale approximations will be described and illustrated. Our recent work on the law of the iterated logarithm and conditional central limit questions will be presented, along with a simple characterization of martingale approximations. As time permits, I will show some of the more interesting ingredients in the proof, featuring operator theory and ergodic theory. (joint work with Michael Woodroofe, University of Michigan)

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