Estimation of proportions of objects and determination of training sample-size in a remote sensing application

A multichannel scanning device may fail to observe objects because of obstructions blocking the view, or different categories of objects may make up a resolution element giving rise to a single observation. Ground truth will be required on any such categories of objects in order to estimate their expected proportions associated with various classes represented in the remote sensing data. Considering the classes to be distributed as multivariate normal with different mean vectors and common covariance, maximum likelihood estimates are given for the expected proportions of objects associated with different classes, using the Bayes procedure for classification of individuals obtained from these classes. An approximate solution for simultaneous confidence intervals on these proportions is given, and thereby a sample-size needed to achieve a desired amount of accuracy for the estimates is determined.