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Seminar on Probability and Statistics Thursday January 19 2017 Tokyo 052 1:00-3:30 pm
Nonparametric Estimation for Self-Exciting Point Processes: A Parsimonious Approach
Feng Chen University of New South Wales Abstract There is ample evidence that in applications of self-exciting
point process (SEPP) models, the intensity of background events is often far
from constant. If a constant background is imposed, that assumption can
reduce significantly the quality of statistical analysis, in problems as
diverse as modelling the after-shocks of earthquakes and the study of
ultra-high frequency financial data. Parametric models can be used to
alleviate this problem, but they run the risk of distorting inference by
misspecifying the nature of the background intensity function. On the other
hand, a purely nonparametric approach to analysis leads to problems of
identifiability; when a nonparametric approach is taken, not every aspect of
the model can be identified from data recorded along a single observed
sample path. In this paper we suggest overcoming this difficulty by using an
approach based on the principle of parsimony, or Occam's razor. In
particular, we suggest taking the point-process intensity to be either a
constant or to have maximum differential entropy. Although seldom used for
nonparametric function estimation in other settings, this approach is
appropriate in the context of SEPP models. (Joint work with the late Peter
Hall.)
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