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SUMMARY:Shrinkage regression for multivariate inference with missing   dat
 a\, with an application to portfolio balancing - Robert B. Gramacy (Univer
 sity of Cambridge)
DTSTART:20090310T150000Z
DTEND:20090310T160000Z
UID:TALK16871@talks.cam.ac.uk
CONTACT:Zoubin Ghahramani
DESCRIPTION:Asset return histories can greatly vary in length. Such data a
 re said to follow a monotone missingness pattern\, which leads to a conven
 ient factorization of the likelihood for the purposes of inference. Under 
 an MVN assumption\, MLEs and samples from a Bayesian posterior can be obta
 ined by repeated OLS regression\, one for each asset. When there are more 
 assets than historical returns (a "big p small n problem")\, however\, OLS
  becomes unstable. We explore remedies that apply shrinkage\, like ridge r
 egression or the lasso\, which have a natural Bayesian implementation\, an
 d can offer improvements in accuracy and interpretation. We focus on the B
 ayesian approach and thus improve upon the work of Stambaugh (1997) to pro
 vide full posterior inference rather than just moments\, in addition to ex
 tending its reach to the "big p small n" setting.  We show how\, in this f
 ramework\, it is straightforward to relax the MVN and monotonicity assumpt
 ions\, incorporate known factors\, test hypotheses about correlation\, obt
 ain credible intervals all parameters in the model and\, in particular\, o
 btain uncertainty bands for the solutions to the quadratic programs using 
 samples from the posterior to\, e.g.\, balance portfolios. Where possible\
 , we provide detailed comparisons to the alternative ML approach.  We conc
 lude with an investment exercise and descriptive analysis based on real fi
 nancial returns data.  An R package implementing all of the methods descri
 bed herein is available on CRAN.\n
LOCATION:Engineering Department\, CBL Room 438
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