B0834
Title: Oracle-efficient estimation for variance function of dense functional data with a smooth simultaneous confidence band
Authors: Li Cai - Zhejiang Gongshang University (China)
Suojin Wang - Texas A and M University (United States)
Suojin Wang - Texas A and M University (United States) [presenting]
Abstract: A new two-step reconstruction-based moment estimator and an asymptotically correct smooth simultaneous confidence band (SCB) is proposed for the heteroscedastic variance function of dense functional data. Step one involves spline smoothing for individual trajectory reconstructions, and step two employs kernel regression on the individual squared residuals to estimate each trajectory variability. Then by the method of moment, an estimator for the variance function of functional data is constructed. The estimation procedure is innovative by synthesizing spline smoothing and kernel regression together, which allows one not only to apply the fast computing speed of spline regression but also to employ the flexible local estimation and the extreme value theory of kernel smoothing. The resulting estimator for the variance function is shown to be oracle-efficient in the sense that it is uniformly as efficient as the ideal estimator when all trajectories were known by ``oracle''. As a result, an asymptotically correct SCB as a global inference tool for the variance function is established. Simulation results support our asymptotic theory with fast computation. As an illustration, the proposed method is applied to the analyses of two real data sets leading to a number of discoveries.
