Partially observed functional data

This article provides a brief overview of statistical methods for analyzing partially observed random functions. We first introduce a formal framework for modeling such data and highlight differences among various observation regimes. In particular, we present a measure-theoretic formulation that generalizes the common "missing at random" assumption to the case of random functions. We then address the estimation of mean and covariance functions, emphasizing conceptual challenges that arise under the partial observation regimes. Finally, we examine the reconstruction of missing fragments. The article reviews some recent contributions and illustrates the theory with two real data sets as well as several examples.