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SUMMARY:Optimal Sup-norm Rates and Uniform Inference on Nonlinear  Functio
 nals of Nonparametric IV Regression - Xiaohong Chen (Yale)
DTSTART:20171124T140000Z
DTEND:20171124T150000Z
UID:TALK87071@talks.cam.ac.uk
CONTACT:Quentin Berthet
DESCRIPTION:This paper makes several important contributions to the litera
 ture about nonparametric instrumental variables (NPIV) estimation and infe
 rence on a structural function h0 and its functionals.\n\nFirst\, we deriv
 e sup-norm convergence rates for computationally simple sieve NPIV (series
  2SLS) estimators of h0 and its derivatives. Second\, we derive a lower bo
 und that describes the best possible (minimax) sup-norm rates of estimatin
 g h0 and its derivatives\, and show that the sieve NPIV estimator can atta
 in the minimax rates when h0 is approximated via a spline or wavelet sieve
 . Our optimal sup-norm rates surprisingly coincide with the optimal root-m
 ean-squared rates for severely ill-posed problems\, and are only a logarit
 hmic factor slower than the optimal root-mean-squared rates for mildly ill
 -posed problems. Third\, we use our sup-norm rates to establish the unifor
 m Gaussian process strong approximations and the score bootstrap uniform c
 onfidence bands (UCBs) for collections of nonlinear functionals of h0 unde
 r primitive conditions\, allowing for mildly and severely ill-posed proble
 ms. Fourth\, as applications\, we obtain the first asymptotic pointwise an
 d uniform inference results for plug-in sieve t-statistics of exact consum
 er surplus (CS) and dead-weight loss (DL) welfare functionals under low-le
 vel conditions when demand is estimated via sieve NPIV. Empiricists could 
 read our real data application of UCBs for exact CS and DL functionals\nof
  gasoline demand that reveals interesting patterns and is applicable to ot
 her markets.
LOCATION:MR12
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