On level and powee of anderson and hauck's peocedure for testing equivalence in compative bioavailability

The paper refers to a new procedure of Anderson and Hauck for the well-known problem of deciding whether two means of normal distributions with common but unknown variance differ within an admissible range. Analytical expressions for level and power of this method are derived and some numerical examples are given. A bound for the difference between real and no¬minal level is obtained which does not involve the variance.     

Manipulating Statistical Hypotheses and Tests as Boolean Functions

Statistical hypotheses and test statistics are Boolean functions that can be manipulated using the tools of Boolean algebra. These tools are particularly useful for exploring multiple comparisons or simultaneous inference theory, in which multiparameter hypotheses or multiparameter test statistics may be decomposed into combinations of uniparameter hypotheses or uniparameter tests. These concepts are illustrated with both finite and infinite decompositions of familiar multiparameter hypotheses and tests. The corresponding decompositions of acceptance regions and rejection regions are also shown. Finally, the close relationship between hypothesis and test decompositions and Roy's union—intersection principle is demonstrated by a derivation of the union—intersection test of the univariate general linear hypothesis.     

空间计量模型视角下环境库兹涅茨曲线形成机理研究

传统的环境库兹涅茨曲线(EKC)在研究中往往隐含着特定地区的环境污染程度彼此独立互相之间不存在关系的假设,这就抹杀了空间因素对环境-经济关系的影响,由此得出的结果也是值得商榷的.为解决这个问题,同时又使环境库兹涅茨曲线研究具有更高的可信度,故采用空间计量的方法,利用综合污染指数作为环境污染指数CPI,并基于2000-2010年的数据对环境库兹涅茨曲线在空间计量的视角下进行研究,得出环境污染存在明显空间相关性的结论.     

On the test of liu and chow's procedure for assessing equivalence in variability of bioavailability

Similar to Schuirmann's two one-sided tests procedure for assessment of bioequivalence in average bioavailability (Schuirmann,), Liu and Chow proposed a two one-sided tests procedure for assessment of equivalence of variability of bioavailability. Their procedure is derived based on the correlation between crossover differences and subject totals. In this paper, we examined the performance of their test procedure in terms of its test size and power for various situations where the intersubject variability and the intrasubject variability of the test drug product are relatively larger, similar, and smaller than that of the intrasubject variability of the reference drug product.     

Tests and confidence intervals for the shape parameter of a gamma distribution

Inference based on the Central Limit Theorem has only first order accuracy. We give tests and confidence intervals (CIs) of second orderaccuracy for the shape parameter ρ of a gamma distribution for both the unscaled and scaled cases.

Tests and CIs based on moment and cumulant estimates are considered as well as those based on the maximum likelihood estimate (MLE).

For the unscaled case the MLE is the moment estimate of order zero; the most efficient moment estimate of integral order is the sample mean, having asymptotic relative efficiency (ARE) .61 when ρ= 1.

For the scaled case the most efficient moment estimate is a functionof the mean and variance. Its ARE is .39 when ρ = 1.

Our motivation for constructing these tests of ρ = 1 and CIs forρ is to provide a simple and convenient method for testing whether a distribution is exponential in situations such as rainfall models where such an assumption is commonly made.     

A glimpse of the impact of pál erd#ous on probability and statistics

The title of this article notwithstanding, it is the author's aspiration here to provide a bit more than merely a glimpse of some of Erdõs's contributions per se to probability‐statistics. He hopes to have succeeded in providing a guided tour of, and whenever it has appeared feasible, an introduction to, a few selected areas that have been strongly influenced by the work of Erdõs. The author also hopes to have succeeded in facilitating a glimpse of the impact of these contributions by presenting them in their historical context.