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SUMMARY:Confidence Bands in Functional data - The Bootstrap or Gaussian Ki
nematic formula?
DTSTART;VALUE=DATE-TIME:20181210T110000Z
DTEND;VALUE=DATE-TIME:20181210T120000Z
UID:https://talks.ox.ac.uk/talks/id/e1e63af1-6d38-4a85-96d6-b95da1a69701/
DESCRIPTION:In this talk we study simultaneous confidence bands (SCBs) for
functional parameters. We introduce a new Multiplier Bootstrap and a "par
ametric approach" using the Gaussian Kinematic Formula (GKF) for construct
ion of SCBs. The GKF as introduced by Jonathan Taylor can be use to approx
imate the distribution of the maximum of Gaussian related processes for la
rge thresholds. One of the main results of this talk will be an error boun
d on the asymptotical coverage rate of SCBs constructed using the GKF\, wh
ich basically requires only a functional CLT for the estimator of the func
tional parameter and some regularity assumptions on the limiting process.\
n\nWe also shortly discuss a strategy how these ideas can be extended to d
iscretely observed functional processes contaminated by observation noise\
, where we build on Scale Spaces introduced by Chaudhuri and Marron in the
early 2000’s.\n\nThe theoretical discussion will be accompanied by simu
lation studies for the population mean in signal plus noise models and an
application of a two sample situation in DTI fibers. In the end we will gi
ve a short outlook on different settings our method can also be applied to
\, e.g. Signal-to-Noise ratios (Cohen's d) or General linear Models\, whic
h are of interest in statistical analysis of fMRI data.
LOCATION:Big Data Institute (Seminar Room 1)\, Old Road Campus OX3 7LF
URL:https://talks.ox.ac.uk/talks/id/e1e63af1-6d38-4a85-96d6-b95da1a69701/
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DESCRIPTION:Talk:Confidence Bands in Functional data - The Bootstrap or Ga
ussian Kinematic formula?
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