Title: An Alternative Approach to Functional Linear Partial Quantile Regression,
Abstract: We have previously proposed the partial quantile regression (PQR) prediction
procedure for functional linear model by using partial quantile covariance
techniques and developed the simple partial quantile regression (SIMPQR)
algorithm to efficiently extract PQR basis for estimating functional
coefficients. However, although the PQR approach is considered as an attractive
alternative to projections onto the principal component basis, there are
certain limitations to uncovering the corresponding asymptotic properties
mainly because of its iterative nature and the non-differentiability of the
quantile loss function. In this article, we propose and implement an
alternative formulation of partial quantile regression (APQR) for functional
linear model by using block relaxation method and finite smoothing techniques.
The proposed reformulation leads to insightful results and motivates new
theory, demonstrating consistency and establishing convergence rates by
applying advanced techniques from empirical process theory. Two simulations and
two real data from ADHD-200 sample and ADNI are investigated to show the
superiority of our proposed methods.