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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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