Remarks on nonstandard least-squares problems

Abstract

It is shown that after treating a least-squares problem in the standard fashion, the imposition of stochastic restrictions on certain parameters can be accomplished essentially by inverting a matrix of an order no larger than the total number of restricted parameters, and that generally there is an explicit term for correcting the unrestricted to the restricted solution. In addition, any known type of nonstandard least-squares adjustment problem can be reduced to an equivalent standard linear problem, that is, one in which there is exactly one observation per condition equation and in which the observations are not correlated.