Mathematics, Statistics, and Computer Science
University of Illinois at Chicago
Spline Confidence Bands for Functional Derivatives
We develop in this paper a new procedure to construct simultaneous confidence bands for derivatives of mean curves in functional data analysis. The technique involves polynomial splines that provide an approximation to the derivatives of the mean functions, the covariance functions and the associated eigenfunctions. We show that the proposed procedure has desirable statistical properties. In particular, we first show that the proposed estimators of derivatives of the mean curves are semiparametrically efficient. Second, we establish consistency results for derivatives of covariance func- tions and their eigenfunctions. Most importantly, we show that the proposed spline confidence bands are asymptotically efficient as if all random trajectories were observed with no error. Finally, the confidence band procedure is illustrated through numerical simulation studies and a real life example. It is a joint work with Drs. Guanqun Cao, Li Wang, and David Todem.
Sponsored by the Department of Mathematical Sciences
Host: Qiongxia (Joanne) Song