We propose a fast covariance smoothing method and associated software that scale up linearly to very large matrices. The main idea is to exploit a very fast new bivariate penalized spline smoothing approach and focus on the practicality and scalability of the method. Currently available methods and software cannot smooth covariance matrices of dimension J > 500, whereas our approach provides fast smoothing for matrices of dimension J > 10; 000. An R function, simulations, and data analysis provide ready to use, reproducible, and scalable tools for practical data analysis of noisy high-dimensional functional data.
Biostatistics | Statistical Methodology
Xiao, Luo; Ruppert, David; Zipunnikov, Vadim; and Crainiceanu, Ciprian, "FAST COVARIANCE ESTIMATION FOR HIGH-DIMENSIONAL FUNCTIONAL DATA" (January 2013). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 249.