Abstract
Let S0 and S1 be random variables distributed independently as σ2χ2(n0) and σ2χ2(n1, λ), respectively, where χ2(n0) denotes the central chi-square distribution with n0 as degree of freedom(d. f.)and χ2(n1, λ) denotes the noncentral chi-square distribution with n1 as d. f. and noncentrality parameter λ. A confidence interval for σ2 is usually constructed based only on S0 and its form is [S0/c2, S0/c1] with c1 and c2 some nonzero constants. A confidence interval based on both S0 and S1 as an improvement to this existing procedure is proposed. It is linked with the Stein's estimator for σ2 which dominates the best equivariant estimator. The improvement of the interval estimation for the ratio of two variances has also been discussed in this paper.
