Evaluation of Confidence Sets for Estimation with Piecewise Linear Constraint

Equality constrained estimation finds its application in problems like positioning of cars on roads. This paper compares two constructions of confidence sets. The first one is given by the intersection of a standard unconstrained confidence set and the constraint, the second one applies the constraint first and designs the confidence set later. Analytical results are presented for a linear constraint. A family of piecewise linear constraints is inspected numerically. It is shown that for the considered scenarios, the second construction with a properly tuned free parameter provides confidence sets that are smaller in the expectation.