Maximizing heritability of a linear combination of traits

In 1971 Jones proposed an approximate procedure for finding that linear combination of scores which has maximum heritability in a twin sample. I give an exact small-sample procedure. I point out two problems: such procedures can over-optimize the heritability by capitalizing on chance, and confidence intervals and significance tests are needed. I give an approach using James-Stein shrinkage estimation and bootstrapped standard errors to address these problems. It appears that confidence intervals may be quite broad. To reduce the width of the confidence intervals, one can accept some small-sample bias in exchange for smaller sampling errors. The James-Stein approach to estimating coefficients is used to achieve reduced confidence interval width. I illustrate with a computational example using personality data.