Patching rainfall data using regression methods .1. Best subset selection, EM and pseudo-EM methods: theory

In this first paper in a set of three, the problem of patching missing values in rainfall records is described, together with some possible solutions, The techniques are confined to regression methods. Two approaches for patching are explored; that based on best subset selection and that based on the expectation-maximisation (EM) algorithm. The background theory and some mathematics are used to justify six different techniques. Comparisons of efficiency and practical implementation are deferred to the second and third papers.