Procedures for Fixed-Width Interval Estimation of the Largest Normal Mean

Single-stage interval estimation of the largest normal mean under heteroscedasnoty

“…The constant d can be obtained from the tables of Chen and Dudewicz (1976) by inverting the entry value in their Tables 1 and 2.…”

“…His idea was extended by Dudewicz and Dalal (1975) to selecting the best normal population in the ranking and selection setting, with unknown and unequal variances (also termed heteroscedasticity). Chen and Dudewicz (1976) and Chen (1977) used the two-stage sampling procedure for developing fixed-width interval estimation on the largest of k normal means under heteroscedasticity. The drawback of the two-stage procedure (as with the sequential procedure) is that one has to take additional samples at the second stage, something which may not be practical in some real problem.…”

A nearly optimal confidence interval for the largest normal mean

“…In the case where variances are known: Dudewicz (1972) and Saxena and Tong (1969) considered symmetric and asymmetric confidence intervals, while Alam, Saxena and Tong (1973) and Dudewicz and Tong (1971) considered optimal confidence intervals. When variances are unknown (equal or unequal) Chen (1977), Chen and Dudewicz (1976) and Tong (1970Tong ( , 1973 considered the problem using two-stage, multistage or sequential sampling procedures. However, when variances a2 are common but unknown, neither exact small sample results nor statistical tables have been obtained except for the large sample approximation by Saxena (1976).…”

Simulation of Coherent Risk Measures

“…We use as a standard the two-stage procedure of Chen and Dudewicz (1976). In the first stage, it samples n 0 observations from each system.…”

“…Our point of departure is the theorem of Chen and Dudewicz (1976) providing a fixed-width, two-sided confidence interval for the maximum µ [k] , based on a two-stage sampling plan. We also draw on results of Nelson et al (2001) to analyze a multi-stage simulation with screening: those systems which are very likely not to be the best are discarded so that thereafter computational resources can be devoted to simulating systems that are more likely to be the best.…”