Consensus mean and interval estimators for the common mean

Rok, strany: 2003, 183 - 194

We consider the problem of interlaboratory studies where the number of measurements made at each laboratory may differ, and, in general, the laboratories may exhibit the between laboratory variability caused by the systematic error due to each laboratory, as well as different within laboratory variances caused by different within laboratory precisions of the measurement methods. In the case when the between laboratory variability can be neglected, we propose two generalized confidence interval estimators ($ {GPV}₁$ and ${GPV}₂$) for the common mean based on the generalized $p$-value approach introduced by Tsui and Weerahandi [ Generalized $p$ values in significance testing of hypotheses in the presence of nuisance parameters, J. Amer. Statist. Assoc. 84 (1989), 602–330] and Weerahandi [ Exact Statistical Methods for Data Analysis, Springer-Verlag, New York, 1995]. The applicability of the suggested estimators is illustrated by a numerical example where the proposed estimators are compared with other two methods: the FW method, see Fairweather [ A method of obtaining an exact confidence interval for the common mean of several normal populations, Applied Statistics 21 (1972), 229–233]. and the JK method, see Jordan and Krishnamoorthy [ Exact confidence intervals for the common mean of several normal populations, Biometrics 52, 1996, 77–86]. The coverage probabilities of the proposed interval estimators were examined using simulations. During the simulation study we have observed that the ${GPV}₁$ interval estimator tends to be anti-conservative and the ${GPV}₂$ generalized confidence interval estimator tends to be conservative. Thus ${GPV}₁$ results in shorter intervals while ${GPV}₂$ leads to longer intervals.

ISO 690:

Witkovský, V., Wimmer, G. 2003. Consensus mean and interval estimators for the common mean. In Tatra Mountains Mathematical Publications, vol. 26, no.1, pp. 183-194. 1210-3195.

APA:

Witkovský, V., Wimmer, G. (2003). Consensus mean and interval estimators for the common mean. Tatra Mountains Mathematical Publications, 26(1), 183-194. 1210-3195.