Inference under Restrictions: Least Squares, Censoring and Errors in Variables Techniques

There are many problems in which a solution would be relatively easier to obtain if there were some additional information recorded or observable. We may, for example, observe a sum of variates of the form Y=X + ε where X and ε are independent. In general, if our observations are distributed according to a convolution, the probability density function may be intractable for maximum likelihood estimation since it may be expressible only as an integral or sum. However, if the components of the sum were observable, then estimation by likelihood methods would often be quite easy.