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)
R E F R E S H M E N T S
4:10 to 4:35 PM
Kenneth W. Anderson
Memorial Reading Room
