Nonparametric inference on smoothed quantile regression process

This paper studies the global estimation in semiparametric quantile regression models. For estimating unknown functional parameters, an integrated quantile regression loss function with penalization is proposed. The first step is to obtain a vector-valued functional Bahadur representation of the resulting estimators, and then derive the asymptotic distribution of the proposed infinite-dimensional estimators. Furthermore, a resampling approach that generalizes the minimand perturbing technique is adopted to construct confidence intervals and to conduct hypothesis testing. Extensive simulation studies demonstrate the effectiveness of the proposed method, and applications to the real estate dataset and world happiness report data are provided. & COPY; 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper investigates global estimation in semiparametric quantile regression models. It proposes an integrated quantile regression loss function with penalization for estimating unknown functional parameters. The first step is to obtain a vector-valued functional Bahadur representation of the resulting estimators, followed by deriving the asymptotic distribution of the proposed infinite-dimensional estimators. Additionally, a resampling approach that generalizes the minimand perturbing technique is used to construct confidence intervals and conduct hypothesis testing. Extensive simulation studies demonstrate the effectiveness of the proposed method, and applications to real estate dataset and world happiness report data are provided.