Function-on-Function Partial Quantile Regression

A function-on-function linear quantile regression model, where both the response and predictors consist of random curves, is proposed by extending classical setting into functional data to characterize entire conditional distribution response. In this paper, a partial approach, analog least squares regression, estimate model. covariance function first used extract basis functions. The extracted functions are then obtain components final Although variables belong an infinite-dimensional space, they observed in finite set discrete-time points practice. Thus, our proposal, forms discretely constructed via finite-dimensional expansion method. using approximated coefficients. method uses iterative procedure components. Bayesian information criterion determine optimum number retained model allows for more than one predictor However, true form unspecified, as relevant unknown forward variable selection significant Moreover, case-sampling-based bootstrap construct pointwise prediction intervals predictive performance evaluated several Monte Carlo experiments under different generation processes error distributions. finite-sample compared with Through empirical example, air quality analyzed demonstrate effectiveness