ABSTRACT
This chapter explores methods for functions which are sparsely observed. In Sparse Functional Data Analysis or S-FDA, smoothing is not applied to individual sparse trajectories. Imputed smooth trajectories can be obtained only after information from the whole sample has been suitably combined. The chapter presents an introductory example which illustrates the differences between nonparametric curve smoothing and the type of smoothing used in sparse FDA. It discusses several options for estimating mean functions in S-FDA, including local polynomial regression, basis functions, and reproducing kernel Hilbert spaces. Local polynomial regression is a special case of kernel smoothing or scatter plot smoothing. Local polynomial regression is a very effective tool for estimating nonlinear mean functions. Sampling designs which are highly unbalanced will result in point-wise variances which are larger in some regions, and smaller in others. Covariance estimation can be viewed as a bivariate version of mean estimation, at least in its implementation.
