A note on interval estimation of the standard deviation of a gamma population with applications to statistical quality control

Traditional process control charts for a measurement standard deviation are based on the assumption of normality, which may not always be valid. Assuming that measurements follow a gamma distribution, we have obtained an approximate distribution of the sample variance, scaled appropriately. This approximate distribution, which happens to be another gamma model, is used to derive an interval estimate of the population standard deviation. Further, the above approximate gamma model for the sample variance can be used to develop a process control chart as demonstrated by a simulated data set.     

Confidence sets and confidence bands for a beta distribution with applications to credit risk management

Incorporating statistical multiple comparisons techniques with credit risk measurement, a new methodology is proposed to construct exact confidence sets and exact confidence bands for a beta distribution. This involves simultaneous inference on the two parameters of the beta distribution, based upon the inversion of Kolmogorov tests. Some monotonicity properties of the distribution function of the beta distribution are established which enable the derivation of an efficient algorithm for the implementation of the procedure. The methodology has important applications to financial risk management. Specifically, the analysis of loss given default (LGD) data are often modeled with a beta distribution. This new approach properly addresses model risk caused by inadequate sample sizes of LGD data, and can be used in conjunction with the standard recommendations provided by regulators to provide enhanced and more informative analyses.     

排序法计算指数寿命型元件串联系统可靠性经典精确最优置信下限

对于样本点是离散的情况,可用对样本点排序的方法确定可靠性置信下限,排序有很多种,有L-P排序、序贯排序、极大似然估计排序、修正L-P排序等。本文提出一种具有直观合理性的新的排序方法,计算指数寿命型元件串联系统可靠性经典精确最优置信下限。     

Computational issues in parameter estimation for stationary hidden Markov models

The parameters of a hidden Markov model (HMM) can be estimated by numerical maximization of the log-likelihood function or, more popularly, using the expectation–maximization (EM) algorithm. In its standard implementation the latter is unsuitable for fitting stationary hidden Markov models (HMMs). We show how it can be modified to achieve this. We propose a hybrid algorithm that is designed to combine the advantageous features of the two algorithms and compare the performance of the three algorithms using simulated data from a designed experiment, and a real data set. The properties investigated are speed of convergence, stability, dependence on initial values, different parameterizations. We also describe the results of an experiment to assess the true coverage probability of bootstrap-based confidence intervals for the parameters.     

Confidence structures in decision making

Decision making is defined in terms of four elements: the set of decisions, the set of outcomes for each decision, a set-valued criterion function, and the decision maker's value judgment for each outcome. Various confidence structures are defined, which give the decision maker's confidence of a given decision leading to a particular outcome. The relation of certain confidence structures to Bayesian decision making and to membership functions in fuzzy set theory is established. A number of schemes are discussed for arriving atbest decisions, and some new types of domination structures are introduced.This research was partly supported by Project No. NR-047-021, ONR Contract No. N-00014-75-C-0569 with the Center for Cybernetic Studies, The University of Texas, Austin, Texas, and by ONR Contract No. N-00014-69-A-0200-1012 with the University of California, Berkeley, California.     

多元线性回归中度量影响的置信域体积比统计量

本文从多元线性回归模型回归系数的椭球置信域出发,导出度量影响的置信域体积比诊断统计量,并给出了它在协方差矩阵未知时的近似表达式。     

Confidence regional method of stochastic spanning tree problem

We consider a P model version of stochastic spanning tree problems with random edge costs. Parameters of underling probability distribution of edge costs are unknown and so they are estimated by a confidence region from statistical data. The problem is first transformed into a deterministic equivalent problem with a minimax type objective function and a confidence region of means and variances, since we assume normal distributions with respect to random edge costs. Our model reflects the situation that the maximum possible damage due to an unknown parameter should be minimized. We show the problem can be reduced to the deterministic equivalent problem of another stochastic spanning tree problem, which is already investigated by us. Thus, we can find an optimal spanning tree of the original problem very efficiently by this reduction.     

A marked difference between two populations under mass screening of neonatal TSH and biotinidase activity

Health-associated reference values are universally needed in clinical chemistry. The aim of this study was to establish the reference intervals of two populations from data obtained by the mass screening of newborn babies and to demonstrate how to determine 95% confidence intervals around the lower and upper limits of reference values from values that are not normally distributed. Biotinidase activities from Belgian (n=260) and Turkish (n=328) populations were measured by fluorometric assay and expressed as 1 IU (1 nmol/(dl min). Neonatal thyroid-stimulating hormone (nTSH) values from Belgian (n=4186) and Turkish (n=1663) populations were also measured by the solid phase two-site fluoroimmunometric assay, the results were given as μU/ml blood. Transformation of data was performed for each parameter. A parametric method was used for determination of reference values of biotinidase activity and the Belgian population was significantly higher than the Turkish population. nTSH reference values were evaluated by an exact non-parametric method, but approximate calculation based on the central limit theorem was also performed for confidence intervals around the reference limits. nTSH values of the Turkish population were found to be significantly higher than for the Belgian population. Rank numbers were found by an exact non-parametric method based upon the assumption of a binomial distribution. This study shows a procedure to define the rank numbers for n>1000 and to obtain reference values with 95% confidence intervals for lower and upper reference limits. Received: 20 July 2002 Accepted: 27 July 2002 Acknowledgements We are grateful to Professor Per Hyloft Peterson, Clinical Biochemist, Odense University Hospital, for his valuable advice and criticism. Also we would like to thank John Pezzullo Associate Professor for Pharmacology and Biostatistics, at Georgetown University Medical Center, for his binomial and approximate calculations. We also want to thank Professor Fatma Kutay, Clinical Chemist, Ege University Medical School and Hospital, for her contributions. This investigation was supported in part by a short term FEBS (Federation European Biochemical Society) fellowship grant. Presented at the European Conference on Quality in the Spotlight in Medical Laboratories, 7–9 October 2001, Antwerp, Belgium Correspondence to T. Tanyal?ın     

Confidence band for expectation dependence with applications

Motivated by the applications of the concept of expectation dependence in economics and finance, we propose a method to construct uniform confidence band for expectation dependence. It is derived based on Hoeffding’s inequality. Our proposed confidence band can be explicitly expressed and thus it is very easy to implement. Our method has applications to demand for a risky asset and first-order risk aversion problems. Simulations suggest our proposed confidence interval can control the coverage probabilities very well, and the average lengths are very short. Two empirical applications are presented to illustrate the usefulness of the constructed confidence band of expectation dependence.     

具有CF2=CF结构的化合物中19F NMR化学位移的计算

系统总结和分析前人对19F NMR化学位移研究成果的基础上,对19F NMR化学位移的规律进行研究,最终确定用回归分析中的最小二乘法来确定计算19F NMR化学位移的公式,并用F检验法对所得计算公式进行检验,给出了具有CF2=CF结构的化合物中19F NMR化学位移的计算公式δcal=B+△α+△β,该公式的置信度为9...