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CATEGORIES:Statistics
SUMMARY:Optimal Sup-norm Rates and Uniform Inference on No
 nlinear  Functionals of Nonparametric IV Regressio
 n - Xiaohong Chen (Yale)
DTSTART;TZID=Europe/London:20171124T140000
DTEND;TZID=Europe/London:20171124T150000
UID:TALK87071AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/87071
DESCRIPTION:This paper makes several important contributions t
 o the literature about nonparametric instrumental 
 variables (NPIV) estimation and inference on a str
 uctural function h0 and its functionals.\n\nFirst\
 , we derive sup-norm convergence rates for computa
 tionally simple sieve NPIV (series 2SLS) estimator
 s of h0 and its derivatives. Second\, we derive a 
 lower bound that describes the best possible (mini
 max) sup-norm rates of estimating h0 and its deriv
 atives\, and show that the sieve NPIV estimator ca
 n attain the minimax rates when h0 is approximated
  via a spline or wavelet sieve. Our optimal sup-no
 rm rates surprisingly coincide with the optimal ro
 ot-mean-squared rates for severely ill-posed probl
 ems\, and are only a logarithmic factor slower tha
 n the optimal root-mean-squared rates for mildly i
 ll-posed problems. Third\, we use our sup-norm rat
 es to establish the uniform Gaussian process stron
 g approximations and the score bootstrap uniform c
 onfidence bands (UCBs) for collections of nonlinea
 r functionals of h0 under primitive conditions\, a
 llowing for mildly and severely ill-posed problems
 . Fourth\, as applications\, we obtain the first a
 symptotic pointwise and uniform inference results 
 for plug-in sieve t-statistics of exact consumer s
 urplus (CS) and dead-weight loss (DL) welfare func
 tionals under low-level conditions when demand is 
 estimated via sieve NPIV. Empiricists could read o
 ur real data application of UCBs for exact CS and 
 DL functionals\nof gasoline demand that reveals in
 teresting patterns and is applicable to other mark
 ets.
LOCATION:MR12
CONTACT:Quentin Berthet
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