Geodesic
Confidence bounds for convex functions of many unknown parameters
Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 2, pp. 394-399

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We find the conditions under which the interval estimation of quasi-convex functions of many unknown parameters with the confidence level more than the given value $\gamma$ may be fulfilled by means of the direct substitution of interval estimates with the same confidence level $\gamma$ into the estimated function. The results are applied to the interval estimation of the function of unknown parameters of normal distribution and to the interval estimation of the reliability of complex system by the results of reliability testing of its components. 
@article{TVP_1980_25_2_a17,
     author = {I. V. Pavlov},
     title = {Confidence bounds for convex functions of many unknown parameters},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {394--399},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1980_25_2_a17/}
}
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I. V. Pavlov. Confidence bounds for convex functions of many unknown parameters. Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 2, pp. 394-399. http://geodesic.mathdoc.fr/item/TVP_1980_25_2_a17/