2021/11/09 by Ufuk Beyaztaş, Han Lin Shang, Beyaztas, Ufuk +1 · 2 citations
Mathematics · #62R10 #Advanced Statistical Methods and Models #Applications (stat.AP) #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2111.05374
openalex publication_date 2021/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this study, we propose a function-on-function linear quantile regression model that allows for more than one functional predictor to establish a more flexible and robust approach. The proposed model is first transformed into a finite-dimensional space via the functional principal component analysis paradigm in the estimation phase. It is then approximated using the estimated functional principal component functions, and the estimated parameter of the quantile regression model is constructed based on the principal component scores. In addition, we propose a Bayesian information criterion to determine the optimum number of truncation constants used in the functional principal component decomposition. Moreover, a stepwise forward procedure and the Bayesian information criterion are used to determine the significant predictors for including in the model. We employ a nonparametric bootstrap procedure to construct prediction intervals for the response functions. The finite sample performance of the proposed method is evaluated via several Monte Carlo experiments and an empirical data example, and the results produced by the proposed method are compared with the ones from existing models.