Missing data treatment using iterative PCA and data reconciliation

Two methods, one based on Iterative Principal Components Analysis(IPCA) and the other based on Data Reconciliation have been developed for estimating a model from a data matrix containing missing data. These algorithms are iterative in nature and analogous to the method based on PCA for treating missing data. The methods incorporate information about the measurement errors to develop the models and are optimal in a maximum likelihood sense. The close connection of the methods with the Expectation Maximization (EM) algorithm is also established. Simulated data from a Flow Network system with a variety of error structures and missing data is used to evaluate the performance of the proposed methods. In all cases, models estimated by the proposed methods were superior to those obtained by the classical PCA-based missing data treatment algorithms for nonuniform error.