A block bootstrap for quasi-likelihood in sparse functional data

This article utilizes bootstrap quasi-likelihood (QL) to model sparse functional data. The proposed method combines parallel block bootstrap and QL to fit the functional data. The parameter space is considered as a finite-dimensional space through a certain optimization rule. Statistical errors of the proposed method are discussed. Some asymptotic properties of the method are established under several mild conditions as well. Several simulations are conducted to examine the finite-sample performance of the method. The performance is also demonstrated by analysing real data.