Statistical aspects of the Chebyshev center estimate

We treat the linear regression problem of estimating theta from noisy observations where the norm of theta is bounded. Instead of using the constrained least-squares approach which minimizes the data error over bounded norm vectors, we explore the use of the Chebyshev-center estimate (CC), that is aimed at minimizing the worst-case squared-error over all bounded-norm vectors theta and bounded noise. We derive an explicit expression for the CC estimate and explore some of its statistical properties. In particular, we show that it can be viewed as a generalized Bayesian estimate where both the parameter vector and the noise have hierarchial Gaussian priors.