We consider several methods of constructing confidence intervals for the noncentrality parameter λ2 of the noncentral chi-squared distribution, based on a single observation, y2. The problem is not straightforward because the parameter space has a finite end-point at λ2 = 0: λ2 is not allowed to be negative, yet λ2 = 0 is feasible. Practical applications include asymptotic interval estimates for multiple correlation coefficients. Bayesian intervals are also discussed. Our overall recommendation is for the use of a ‘symmetric range’ confidence interval.
Confidence intervals for the noncentral chi-squared distribution