One of the problems in remote sensing is estimating the expected proportions of certain categories of objects which cannot be observed directly or distinctly. For example, a multi-channel 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. This will require ground truth on any such categories of objects for estimating 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, we give the maximum likelihood estimates 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 has been determined.

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