Robin Willink

Industrial Research Ltd

A general construction of a shrinkage confidence interval

This paper describes the construction of confidence interval that is narrower than a standard interval when a prior guess, theta_0, for an unknown univariate parameter theta is sufficiently accurate. This confidence interval is obtained through moving one or both of the limits of a standard interval toward theta_0. A general procedure for the construction of such a `shrinkage confidence interval' is given for suitable univariate problems. When theta_0 is close to theta, the technique can achieve an interval with mean width considerably smaller than that of the corresponding standard interval.

This paper builds on work described in `Shrinkage confidence intervals for the normal mean: using a guess for greater efficiency', R. Willink, Canadian Journal of Statistics, 36, No 4, (2008) 623-638. (Note: This form of shrinkage estimation is to be distinguished from James-Stein estimation.)