Isobar separation at FRS-ESR – a development towards pure isomeric stored beams

One important goal of the ILIMA project at FAIR is the study of masses and decay properties of relativistic isomeric beams stored and cooled in the planned storage-ring complex. A new scheme is described, where a storage-cooler ring is used for high-resolution mass separation. Experimental results on the separation of the isobaric pair ¹⁴⁰Pr-¹⁴⁰Ce are presented. P. Beller, deceased.     

Solubility of Anthraquinone Derivatives in Supercritical Carbon Dioxide: New Correlations

Solubility of several anthraquinone derivatives in supercritical carbon dioxide was readily available in the literature, but correcting ability of the existing models was poor. Therefore, in this work, two new models have been developed for better correlation based on solid–liquid phase equilibria. The new model has five adjustable parameters correlating the solubility isotherms as a function of temperature. The accuracy of the proposed models was evaluated by correlating 25 binary systems. The proposed models observed provide the best overall correlations. The overall deviation between the experimental and the correlated results was less than 11.46% in averaged absolute relative deviation (AARD). Moreover, exiting solubility models were also evaluated for all the compounds for the comparison purpose.     

Multi-sample cluster analysis using Akaike's Information Criterion

Summary Multi-sample cluster analysis, the problem of grouping samples, is studied from an information-theoretic viewpoint via Akaike's Information Criterion (AIC). This criterion combines the maximum value of the likelihood with the number of parameters used in achieving that value. The multi-sample cluster problem is defined, and AIC is developed for this problem. The form of AIC is derived in both the multivariate analysis of variance (MANOVA) model and in the multivariate model with varying mean vectors and variance-covariance matrices. Numerical examples are presented for AIC and another criterion calledw-square. The results demonstrate the utility of AIC in identifying the best clustering alternatives. This research was supported by Office of Naval Research Contract N00014-80-C-0408, Task NR042-443 and Army Research Office Contract DAAG 29-82-K-0155, at the University of Illinois at Chicago.     

Selection of the number of regression variables; A minimax choice of generalized FPE

Summary A generalized Final Prediction Error (FPE_α)_ criterion is considered. Based onn observations, the numberk of regression variables is selected from a given range 0≦k≦K, so as to minimize . It is shown that if α tends to infinity withn, the selection is consistent but the maximum of the mean squared error of estimates of parameters diverges to infinity with the same order of divergence as that of α. A meaningful minimax choice of α exists for a regret type mean squared error, while for simple mean squared error it is trivially 0. The minimax regret choice of α converges to a constant, approximately 3.5 forK≧8 ifn−K increases simultaneously withn, otherwise it diverges to infinity withn.     

实证研究中预测模型的选择:从逐步回归到信息标准

本文首先对显著性变量同变量显著性之间的关系予以讨论并区分,进而评价逐步回归模型选择法的缺陷性。在此基础上,我们对以AIC和B IC为代表的各种基于信息标准的模型选择法予以介绍和评论。同逐步回归法相比,信息标准模型选择法有着坚实的统计理论基础及清晰而优良的统计性质。本文通过基于近十年中国股市数据的实证检验说明,信息标准同逐步回归相比往往能产生具有更强预测能力的计量模型,因此值得在未来的实证研究中注意并推广。     

Order Determination for Multivariate Autoregressive Processes Using Resampling Methods

LetX₁, …, X_nbe observations from a multivariate AR(p) model with unknown orderp. A resampling procedure is proposed for estimating the orderp. The classical criteria, such as AIC and BIC, estimate the orderpas the minimizer of the function[formula]wherenis the sample size,kis the order of the fitted model, Σ²_kis an estimate of the white noise covariance matrix, andC_nis a sequence of specified constants (for AIC,C_n=2m²/n, for Hannan and Quinn's modification of BIC,C_n=2m²(ln ln n)/n, wheremis the dimension of the data vector). A resampling scheme is proposed to estimate an improved penalty factorC_n. Conditional on the data, this procedure produces a consistent estimate ofp. Simulation results support the effectiveness of this procedure when compared with some of the traditional order selection criteria. Comments are also made on the use of Yule–Walker as opposed to conditional least squares estimations for order selection.     

Bayesian analysis of lymphatic spreading patterns in cancer of the thoracic esophagus

For the treatment of patients with cancer of the thoracic esophagus, lymphatic spreading is one important factor to infer how advanced their cancer is. We introduced a one-dimensional scale based on lymphatic spreading patterns, the stage of cancer, to express how advanced their cancer is, and we proposed a method to infer each patient's stage from his lymphatic spreading pattern by applying a Bayesian model. Our Bayesian model was built based on the assumption that lymphatic spreading in cancer could be explained as what was brought about by the advance of stage. In the modeling, we introduced the probability of what stage each patient was in as a prior distribution. We also introduced distribution functions of Weibull distributions to express the relation between the advance of stage and the increase of the probability of metastasis. Our model was applied to the data of nodal involvement obtained from 103 patients with cancer of the thoracic esophagus and the parameters were estimated with the maximum likelihood method. AIC was used to check that the data had enough information to be divided into the stages of a clinically reasonable number. With the estimated parameters, we inferred the probability of metastasis to each lymph node in each stage and calculated by Bayes' theorem with 31 new patients the probability of what stage they were in. The results well represented some characteristics of the lymphatic spreading and suggested the appropriateness of our approach.The present study was carried out under the ISM Cooperative Research Program (91-ISM·CRP-18).     

Bootstrapping Likelihood for Model Selection with Small Samples

Abstract

Akaike's information criterion (AIC), derived from asymptotics of the maximum likelihood estimator, is widely used in model selection. However, it has a finite-sample bias that produces overfitting in linear regression. To deal with this problem, Ishiguro, Sakamoto, and Kitagawa proposed a bootstrap-based extension to AIC which they called EIC. This article compares model-selection performance of AIC, EIC, a bootstrap-smoothed likelihood cross-validation (BCV) and its modification (632CV) in small-sample linear regression, logistic regression, and Cox regression. Simulation results show that EIC largely overcomes AIC's overfitting problem and that BCV may be better than EIC. Hence, the three methods based on bootstrapping the likelihood establish themselves as important alternatives to AIC in model selection with small samples.     

Application of Kalman Filter Finite Element Method and AIC

This paper presents a numerical simulation for application of the Kalman filter finite element method. The Kalman filter is employed frequently for the solution of time series analysis including observation and system noises. Applying the Kalman filter to the finite element method, the present method is capable of the estimation in time and space directions. In this method, the matrix generated by the finite element method is applied to the state transition matrix. Using the Kalman filter finite element method, the characteristics of both the Kalman filter and the finite element method can be strengthened. In this paper, the state transition matrix is based on the shallow water equations which are approximated by the finite element method. This method can estimate the tidal current not only in time but also in space directions.     

Minimaxity of a preliminary test estimator for the mean of normal distribution

Summary The problem is to estimate the mean of the normal distribution under the situation where there is vague information that the mean might be equal to zero. A minimax property of the preliminary test estimator obtained by the use of AIC (Akaike information Criterion) procedure is proved under a loss function based on the Kullback-Leibler information measure.