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CATEGORIES:Statistics
SUMMARY:Conditional Predictive Inference Post-Model Select
ion - Hannes Leeb (Univ. Vienna)
DTSTART;TZID=Europe/London:20091204T160000
DTEND;TZID=Europe/London:20091204T170000
UID:TALK20014AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/20014
DESCRIPTION:We give a finite-sample analysis of predictive inf
erence procedures\n after model selection
in regression with random design. The\n an
alysis\n is focused on a statistically cha
llenging scenario where the number\n of po
tentially important explanatory variables can be i
nfinite\,\n where\n no regularity
conditions are imposed on unknown parameters\, whe
re\n the number of explanatory variables i
n a `good' model can be of\n the same orde
r as sample size\, and where the number of candida
te\n models can be of larger order than sa
mple size. The performance of\n inference
procedures is evaluated conditional on the trainin
g\n sample.\n Under weak condition
s on only the number of candidate models and\n
on their complexity\, and uniformly over all
data-generating\n processes\n unde
r consideration\, we show that a certain predictio
n interval is\n approximately valid and sh
ort with high probability in finite\n samp
les\,\n in the sense that its actual cover
age probability is close to the\n nominal
one\, and in the sense that its length is close to
the\n length\n of an infeasible i
nterval that is constructed by actually knowing\n
the 'best' candidate model. Similar result
s are shown to hold for\n predictive infer
ence procedures other than prediction intervals\n
like\,\n e.g.\, tests of whether a
future response will lie above or below a\n
given threshold.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Richard Nickl
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