Confidence Intervals for Inequality-Constrained Least Squares Problems, with Applications to Ill-Posed Problems

Computing confidence intervals for functions $\phi (x) = w^T x$, where $Kx = y + e$ and e is a normally distributed error vector, is a standard problem in multivariate statistics. In this work, we develop an algorithm for solving this problem if additional information, $x \geqq 0$, is given. Applications to estimating solutions to integral equations of the first kind are given.

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