APPROXIMATE CONFIDENCE-INTERVALS ON POSITIVE LINEAR-COMBINATIONS OF EXPECTED MEAN SQUARES

Let n(i)S(i)2/theta-i for i = 1,2,..., q represent independently distributed chi-squared random variables with n(i) degrees of freedom. In this article, we develop new procedures for obtaining approximate confidence intervals on positive linear combinations of the theta-i. The proposed approximations, in many cases, are the weighted average of liberal and conservative confidence limits. By choosing the appropriate weight, which can be easily determined from data, we show that the proposed methods produce confidence intervals with confidence coefficients very close to the stated level. Numerical examples compare the performance to other approximations.