DETECTION AND ESTIMATION OF LOCAL SIGNALS

DAVID SIEGMUND – STANFORD UNIVERSITY

ABSTRACT

The maximum score statistic is used to detect and estimate local signals in the form of change-points in the level, slope, or other property of a sequence of observations, and to segment the sequence when there appear to be multiple changes. Control of false positive errors when observations are temporally dependent is achieved by means of a first order autoregressive model, but true changes in level or slope can lead to badly biased estimates of the autoregressive parameter, resulting in a loss of power. I suggest modifications of the natural estimator to deal with this difficulty, with partial success. Applications to temperature variations, atmospheric CO2 levels, disease incidence, and fluctuations in the size of animal populations illustrate the general theory.

This is joint research with Xiao Fang.