A0540
Title: Gaussian approximation for high-dimensional u-statistics with size-dependent kernels
Authors: Shunsuke Imai - Kyoto University - Graduate School of Economics (Japan) [presenting]
Yuta Koike - University of Tokyo (Japan)
Abstract: Motivated by small bandwidth asymptotics for kernel-based semiparametric estimators in econometrics, Gaussian approximation results are established for high-dimensional fixed-order U-statistics whose kernels depend on the sample size. Results allow for a situation where the dominant component of the Hoeffding decomposition is absent or unknown, including cases with known degrees of degeneracy as special forms. The obtained error bounds for Gaussian approximations are sharp enough to almost recover the weakest bandwidth condition of small bandwidth asymptotics in the fixed-dimensional setting when applied to a canonical semiparametric estimation problem. An application to adaptive goodness-of-fit testing is also presented, along with discussions about several potential applications.
