The Nonexistence of Procedures with Bounded Performance Characteristics in Certain Parametric Inference Problems

This paper gives a condition which implies the nonexistence of parametric statistical procedures with bounded risk or error performance characteristics. Many examples for which such a condition is satisfied are considered.     

Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones

We study the problem of existence of regions separating a given amount of volume with the least possible perimeter inside a Euclidean cone. Our main result shows that nonexistence for a given volume implies that the isoperimetric profile of the cone coincides with the one of the half-space. This allows us to give some criteria ensuring existence of isoperimetric regions: for instance, local convexity of the cone at some boundary point.

We also characterize which are the stable regions in a convex cone, i.e., second order minima of perimeter under a volume constraint. From this it follows that the isoperimetric regions in a convex cone are the euclidean balls centered at the vertex intersected with the cone.

     

Confidence regions in a multivariate regression model with constraints II

The multivariate model, where not only parameters of the mean value of the observation matrix, but also some other parameters occur in constraints, is considered in the paper. Some basic inference is presented under the condition that the covariance matrix is either unknown, or partially unknown, or known. Supported by the grant of the Council of Czech Republic MSM 6 198 959 214.     

串联系统可靠性虚拟系统法置信下限的小样本性质

本文讨论了具有r个成败型元件串联系统可靠性的置信下限问题。研究了虚拟系统法置信下限的小样本性质,证明了,在通常情况下虚拟系统法置信下限要大于常见的L-M法置信下限.更一般地,本文证明了在成败型试验中,当成功数与试验数之比保持不变时,试验次数的增加将直接缩小成功率置信区间的长度。     

火工品可靠性试验数据的综合分析方法

升降法试验数据和固定刺激量下的成败型试验数据,是两种最常见的火工品可靠性试验数据．我们应用Markov链,研究了升降法试验数据下,感度分布参数的极大似然估计的特性．在此基础上,应用Bootstrap方法和Bayes方法,给出了综合分析两种试验数据的方法．最后,将该方法应用于520底火的可靠性鉴定,得出了有益的结论．     

A transport model for the evolution of urban systems

When comparing an urban system to an elasto-plastic lattice, an analogy to the solid state of matter can be exploited using the concepts of the band theory similarly. Thereafter, the population dynamics – in a region of certain stability in the state space and within appropriate energy bands – can be described in terms of Cellular Automata, with two mobile agents or pseudo particles: the inhabitant (representative of an average individual) and the recurson (representative of its multidimensional resources). As in the solid state, transition rules take the form of two coupled transport equations, comprising the terms equivalent to the generation-recombination and circulation processes. The first process can be compared to a predator–prey growth model, typical of Ecology; whereas the circulation process – composed of a drift component and a diffusion component – should be compared to the concentration-sprawl demographic balance seen in urban occupation and dynamics. Thus, it needs to be defined and determined an urban potential function, an equivalent population charge, mobility and diffusion parameters, as well as net growth factors. This analogy, discussed within the context of a case study for Great Mendoza, plausibly explains the varied growth rates of the political departments, as well as the principal urban trends for spatial occupation.     

Interval estimation of the critical value in a general linear model

Summary This paper concerns interval estimation of the critical value θ which satisfies under the general linear model,Y _i =μ(x _i )+ε _i (i=1,2,···), where for and the functional forms off _j ^′ s are known. From an asymptotic expansion it is shown that, under reasonable conditions, the limiting distribution of is normal. Thus in the large-sample case a confidence interval for θ can be obtained. Such a result is useful when one is interested in carrying out a retrospective analysis rather than designing the experiment (as in the Kiefer-Wolfowitz procedure). In Section 3 a sequential procedure is considered for confidence intervals with fixed width 2d. It is shown that, for a given stopping variableN, is also asymptotically normal asd→0. Thus the coverage probability converges to 1−α (preassigned) asd→0. An example of application in estimating the phase parameter in circadian rhythms is given for the purpose of illustration. Research partially supported by the NSF Grant DMS-8502346.     

Some selected problems of nonaqueous microemulsions — phase diagrams and variation of the composition in the quaternary and ternary systems

A variety of quaternary and ternary systems of the type of dodecane/aliphatic alcohols/Na-dodecyl sulphate/water or a water-replacing component (formamide, ethylene glycol, propylene glycol, propylene carbonate, dimethylsulfoxide, acetonitrile) were subjected to a comparative analysis of microemulsification. The compositions of the systems of the type of oil/surfactant/cosurfactant/water or nonaqueous liquid were changed with respect to surfactant (Na-dodecyl sulfate and triton X 114) concentration, cosurfactant (homologous aliphatic alcohols) concentration and mixing ratio of water and water-replacing component. The appertaining phase diagrams were plotted and compared with those of aqueous systems.The experimental results suggest that the phase regions, which are designated as nonaqueous microemulsions, probably represent, not only microemulsions in the usual sense, but a separate kind of mixed phase whose microstructure is examined by special studies. Analogously to aqueous microemulsion systems, transparency and spontaneous formation of homogeneous multicomponent systems cannot serve as the sole criteria for waterless microemulsion formation. But they are important guiding properties of microemulsion formation in multicomponent systems.The variety of components involved in the chemical composition and the current insufficient knowledge do not permit to generally decide whether nonaqueous systems can be assigned to microemulsions or to molecular solutions. For clarifying this problem a detailed examination of the miscibility behavior, especially that of binary systems as a function of temperature, and the role that surfactant and cosurfactant play in the formation of homogeneous systems will be necessary.     

Likelihood Inference under Generalized Hybrid Censoring Scheme with Comp eting Risks

Statistical inference is developed for the analysis of generalized type-II hybrid censoring data under exponential competing risks model. In order to solve the problem that approximate methods make unsatisfactory performances in the case of small sample size, we establish the exact conditional distributions of estimators for parameters by conditional moment generating function(CMGF). Furthermore, confidence intervals(CIs) are constructed by exact distributions, approximate distributions as well as bootstrap method respectively, and their performances are evaluated by Monte Carlo simulations. And finally, a real data set is analyzed to illustrate all the methods developed here.     

Isotopic Characterization of 100% Agave Tequila (Silver,Aged and Extra-Aged Class) for Its Use as an Additional Parameter in the Determination of the Authenticity of the Beverage Maturation Time

Isotopic ratios of δ¹³C_VPDB and δ¹⁸O_VSMOW have been used as an additional parameter to ensure the authenticity of the aging time of 100% agave tequila. For this purpose, 120 samples were isotopically analyzed (40 silver class, 40 aged class, and 40 extra-aged classes). The samples were obtained through a stratified sampling by proportional allocation, considering tequila producers from the main different regions of Jalisco, Mexico (Valles 41%, Altos Sur 31%, Cienega 16%, and Centro 12%). The results showed that the δ¹³C_VPDB was found in an average of −12.85 ‰ for all the analyzed beverages, with no significant difference between them. Since for all the tested samples the Agave tequilana Weber blue variety was used as source of sugar to obtain alcohol, those results were foreseeable, and confirm the origin of the sugar source. Instead, the results for δ¹⁸O_VSMOW showed a positive slope linear trend for the aging time (silver class 19.52‰, aged class 20.54‰, extra-aged class 21.45‰), which is associated with the maturation process, there are oxidation reactions that add congeneric compounds to the beverage, these can be used as tracers for the authenticity of the aging time. Additionally, the experimental data showed homogeneity in the beverages regardless of the production region, evidencing the tequila industry’s high-quality standards. However, a particular case occurs with the δ¹⁸O_VSMOW data for the silver class samples, in which a clear trend is noted with the altitude of the region of origin; therefore, this information suggests that this analytical parameter could be useful to authenticate the regional origin of beverage.