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SUMMARY:Conditional Predictive Inference Post-Model Selection - Hannes Lee
 b (Univ. Vienna)
DTSTART:20091204T160000Z
DTEND:20091204T170000Z
UID:TALK20014@talks.cam.ac.uk
CONTACT:Richard Nickl
DESCRIPTION:We give a finite-sample analysis of predictive inference proce
 dures\n         after model selection in regression with random design. Th
 e\n         analysis\n         is focused on a statistically challenging s
 cenario where the number\n         of potentially important explanatory va
 riables can be infinite\,\n         where\n         no regularity conditio
 ns are imposed on unknown parameters\, where\n         the number of expla
 natory variables in a `good' model can be of\n         the same order as s
 ample size\, and where the number of candidate\n         models can be of 
 larger order than sample size. The performance of\n         inference proc
 edures is evaluated conditional on the training\n         sample.\n       
   Under weak conditions on only the number of candidate models and\n      
    on their complexity\, and uniformly over all data-generating\n         
 processes\n         under consideration\, we show that a certain predictio
 n interval is\n         approximately valid and short with high probabilit
 y in finite\n         samples\,\n         in the sense that its actual cov
 erage probability is close to the\n         nominal one\, and in the sense
  that its length is close to the\n         length\n         of an infeasib
 le interval that is constructed by actually knowing\n         the 'best' c
 andidate model. Similar results are shown to hold for\n         predictive
  inference 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 0WB
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