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SUMMARY:High Dimensional Influence Measure - Chenlei Leng\, University of 
 Warwick
DTSTART:20131206T160000Z
DTEND:20131206T170000Z
UID:TALK47613@talks.cam.ac.uk
CONTACT:20082
DESCRIPTION:Influence diagnosis is important since presence of influential
  observations could lead to distorted analysis and misleading interpretati
 ons. For high dimensional data\, it is particularly so\, as the increased 
 dimensionality and complexity may amplify both the chance of an observatio
 n being influential\, and its potential impact on the analysis. In this ar
 ticle\, we propose a novel high dimensional influence measure for regressi
 ons with the number of predictors far exceeding the sample size. Our propo
 sal can be viewed as a high dimensional counterpart to the classical Cook'
 s distance. However\, whereas the Cook's distance quantifies the individua
 l observation's influence on the least squares regression coefficient esti
 mate\, our new diagnosis measure captures the influence on the marginal co
 rrelations\, which in turn exerts serious influence on downstream analysis
  including coefficient estimation\, variable selection and screening. More
 over\, we establish the asymptotic distribution of the proposed influence 
 measure by letting the predictor dimension go to infinity. Availability of
  this asymptotic distribution leads to a principled rule to determine the 
 critical value for influential observation detection. Both simulations and
  real data analysis demonstrate usefulness of the new influence diagnosis 
 measure.
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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