Confidence intervals for the noncentral chi-squared distribution. (English) Zbl 0832.62025
Summary: We consider several methods of constructing confidence intervals for the noncentrality parameter \(\lambda^2\) of the noncentral chi-squared distribution, based on a single observation, \(y^2\). The problem is not straightforward because the parameter space has a finite end-point at \(\lambda^2 = 0 : \lambda^2\) is not allowed to be negative, yet \(\lambda^2 = 0\) 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.
MSC:
| 62F25 | Parametric tolerance and confidence regions |
| 62H20 | Measures of association (correlation, canonical correlation, etc.) |
Keywords:
information gain; product moment correlation; confidence intervals; noncentrality parameter; noncentral chi-squared distribution; asymptotic interval estimates; multiple correlation coefficients; Bayesian intervalsReferences:
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