Accelerated life tests under competing weibull causes of failure

Accelerated life testing of a product under more severe than normal conditions is cawiionly used to reduce test time and cost. Data collected at such accelerated conditions is used to obtain estimates of parameters of a stress translation function which is then used to make inference about the product's, per" formance under normal conditions. This problem is considered when the product is a p component series system with WeibuH distributed component lifetimes liaving a caimon shape parameter. A general stress translation function is used and estimates of model parameters are obtained for various censoring schemes.     

A comparison of maximum likelihood and least squares for the estimation of a cumulative distribution

Monte Carlo methods are used to compare the methods of maximum likelihood and least squares to estimate a cumulative distribution function. When the probabilistic model used is correct or nearly correct, the two methods produce similar results with the MLE usually slightly superior When an incorrect model is used, or when the data is contaminated, the least squares technique often gives substantially superior results.     

Bounds of moment generating functions of some life distributions

In this article we show that if a life has new better than used in expectation (NBUE) ageing property and if the mean life is finite then the moment generating function exists and is finite. In fact, the moment generating function is shown to be bounded above by that of the exponential distribution with the same mean. Analogous results are also proven for two much bigger families of life distribution, namely, the new better than renewal used in expectation (NBRUE) and the renewal new is better than used in expectation (RNBUE) and the renewal new better than renewal used in expectation (RNBRUE), provided that the life has finite two moments. Further, stronger results are also obtained for the smaller new better than used version of the above classes.     

Robust estimation of complicated profiles using wavelets

Some quality characteristics are well defined when treated as the response variables and their relationships are identified to some independent variables. This relationship is called a profile. The parametric models, such as linear models, may be used to model the profiles. However, due to the complexity of many processes in practical applications, it is inappropriate to model the process using parametric models. In these cases non parametric methods are used to model the processes. One of the most applicable non parametric methods used to model complicated profiles is the wavelet. Many authors considered the use of the wavelet transformation only for monitoring the processes in phase II. The problem of estimating the in-control profile in phase I using wavelet transformation is not deeply addressed. Usually classical estimators are used in phase I to estimate the in-control profiles, even when the wavelet transformation is used. These estimators are suitable if the data do not contain outliers. However, when the outliers exist, these estimators cannot estimate the in-control profile properly. In this research, a robust method of estimating the in-control profiles is proposed, which is insensitive to the presence of outliers and could be applied when the wavelet transformation is used. The proposed estimator is the combination of the robust clustering and the S-estimator. This estimator is compared with the classical estimator of the in-control profile in the presence of outliers. The results from a large simulation study show that using the proposed method, one can estimate the in-control profile precisely when the data are contaminated either locally or globally.     

Covariate selection for estimating the causal effect of control plans by using causal diagrams

Summary. Consider a case where cause–effect relationships between variables can be described by a causal path diagram and the corresponding linear structural equation model. The paper proposes a graphical selection criterion for covariates to estimate the causal effect of a control plan. For designing the control plan, it is essential to determine both covariates that are used for control and covariates that are used for identification. The selection of covariates used for control is only constrained by the requirement that the covariates be non-descendants of a treatment variable. However, the selection of covariates used for identification is dependent on the selection of covariates used for control and is not unique. In the paper, the difference between covariates that are used for identification is evaluated on the basis of the asymptotic variance of the estimated causal effect of an effective control plan. Furthermore, the results can be also described in terms of a graph structure.     

引力模型的应用：服务贸易国际竞争力度量

服务贸易国际竞争力是进行服务贸易国际比较的重要评价指标,大多数学者利用已有指标对服务贸易国际竞争力进行了测算,但现有的竞争力指标不适合服务贸易国际竞争力的评价。故基于引力模型理论,建立了服务贸易国际竞争力度量的新方法,并通过实证分析得出：总体上中国服务贸易竞争力走强,但现代服务贸易的行业竞争力非常弱的结论。     

Weibull accelerated life tests when there are competing causes of failure

Accelerated life testing of a product under more severe than normal conditions is commonly used to reduce test time and costs. Data collected at such accelerated conditions are used to obtain estimates of the parameters of a stress translation function. This function is then used to make inference about the product's life under normal operating conditions. We consider the problem of accelerated life tests when the product of interest is a p component series system. Each of the components is assumed to have an independent Weibull time to failure distribution with different shape parameters and different scale parameters which are increasing functions stress. A general model i s used for the scale parameter includes the standard engineering models as special This model also has an appealing biological interpretation     

Empirical Bayes models of Poisson clinical trials and sample size determination

Bayesian methods are often used to reduce the sample sizes and/or increase the power of clinical trials. The right choice of the prior distribution is a critical step in Bayesian modeling. If the prior not completely specified, historical data may be used to estimate it. In the empirical Bayesian analysis, the resulting prior can be used to produce the posterior distribution. In this paper, we describe a Bayesian Poisson model with a conjugate Gamma prior. The parameters of Gamma distribution are estimated in the empirical Bayesian framework under two estimation schemes. The straightforward numerical search for the maximum likelihood (ML) solution using the marginal negative binomial distribution is unfeasible occasionally. We propose a simplification to the maximization procedure. The Markov Chain Monte Carlo method is used to create a set of Poisson parameters from the historical count data. These Poisson parameters are used to uniquely define the Gamma likelihood function. Easily computable approximation formulae may be used to find the ML estimations for the parameters of gamma distribution. For the sample size calculations, the ML solution is replaced by its upper confidence limit to reflect an incomplete exchangeability of historical trials as opposed to current studies. The exchangeability is measured by the confidence interval for the historical rate of the events. With this prior, the formula for the sample size calculation is completely defined. Published in 2009 by John Wiley & Sons, Ltd.     

中国各地区经济发展水平的实证分析

利用1995-2006年数据,采用时序多指标综合评价法,对中国各地区经济发展水平进行评价研究。结论表明：虽然中国1995-2006年经济增长迅速,但是经济发展水平并未得到显著提高;各地区经济发展不均衡,地域差距较大且有逐年扩大的倾向。     

Canonical analysis of soil data

Canonical variate analysis is used to explore the similarities and differences between a priori soil groups on the basis of laboratory measurements of soil properties and the growth of seedlings in the soils. Canonical correlation is used to relate the growth of the seedlings to the soil properties.     

An Approximation for the Test of the Equality of the Smallest Eigenvalues of a Covariance Matrix

A limiting distribution of the likelihood ratio statistic for the test of the equality of the q smallest eigenvalues of a covariance matrix is obtained. This distribution can be used as an alternative to the chi-squared distribution which is usually used with this test. It is shown that this new method yields reasonable significance levels for those situations in which the chi-squared approximation is inadequate.     

Control variates for monte carlo analysis of nonlinear statisticalmodels. IV

A Monte Carlo control variate method is used to study the estimators obtained in nonlinear regression under nonnormal error distributions. Two forms of the standard linear approximator are used as the control variates: a natural approximator using the nonnormal errors sampled, and a normalized approximator obtained by transformation of the errors. The natural approximator is shown to be most effective when the sampling distribution is itself nonnormal; its effectiveness is well approximated by a function of the Beale measure of nonlinearity. The normalized approximator is most effective when the estimator sampling distribution is approximately normal. A one-parameter model is used for illustration with uniform and gamma distributed errors     

Estimation of sample selection bias models

Econometric models with sample selection biases are widely used in various fields of economics, such as labor economics. The Maximum Likelihood Estimator (MLE) is seldom used to estimate models because of computational difficulty, while Heckman's two-step estimator is widely used to estimate these models. However, Heckman's two-step estimator sometimes performs poorly. In this paper, methods of calculating the MLE are analysed, and finite sample properties of the MLE and Heckman's two-step estimator are compared using Monte Carlo experiments and empirical examples.     

Bayesian volumetric calibration: an application of reversible jump Markov chain Monte Carlo methods

Volumetric calibration is used for high accuracy estimation of the functional volume-to-level relationship for vessels used to store hazardous liquids. An example of calibration of a vessel for reprocessed nuclear material is used to illustrate an analysis of calibration data. We advocate a Bayesian approach, with proper account of genuine prior information, using a reversible jump Markov chain Monte Carlo method for estimation.     

Bayesian prediction of future number of failures based on finite mixture of general class of distributions

This paper is concerned with the Bayesian prediction problem of the number of components which will fail in a future time interval. The failure times are distributed according to a finite mixture of a general class of distributions. Type-I censored sample from this nonhomogeneous population and a general class of prior density functions are used. A one-sample scheme is used to predict the number of failures in a future time interval. An example of a finite mixture of k exponential components is given to illustrate our results.     

An investigation of a quadratic design criterion for estimation of the hemodynamic response function

Optimal experimental design for estimation of the hemodynamic response function (HRF) is investigated using a nonlinear model with a quadratic mean squared error design criterion. This criterion is used, along with a genetic algorithm, to select locally optimal designs that are shown to be, in most cases, more efficient than designs selected with the more commonly used linear expansion criterion. These designs are also shown to result in lower overall asymptotic estimator variance and bias. The investigation focuses on a single stimulus type, but the criterion can also be used with multiple stimulus types.     

Flexible modeling of conditional distributions using smooth mixtures of asymmetric student t densities

A general model is proposed for flexibly estimating the density of a continuous response variable conditional on a possibly high-dimensional set of covariates. The model is a finite mixture of asymmetric student t densities with covariate-dependent mixture weights. The four parameters of the components, the mean, degrees of freedom, scale and skewness, are all modeled as functions of the covariates. Inference is Bayesian and the computation is carried out using Markov chain Monte Carlo simulation. To enable model parsimony, a variable selection prior is used in each set of covariates and among the covariates in the mixing weights. The model is used to analyze the distribution of daily stock market returns, and shown to more accurately forecast the distribution of returns than other widely used models for financial data.     

Asymptotic normality of generalized maximum spacing estimators for multivariate observations

In this paper, the maximum spacing method is considered for multivariate observations. Nearest neighbor balls are used as a multidimensional analogue to univariate spacings. A class of information-type measures is used to generalize the concept of maximum spacing estimators of model parameters. Asymptotic normality of these generalized maximum spacing estimators is proved when the assigned model class is correct, that is, the true density is a member of the model class.     

Identification of factors influencing dispersion in split-plot experiments

As split-plot designs are commonly used in robust design it is important to identify factors in these designs that influence the dispersion of the response variable. In this article, the Bergman-Hynén method, developed for identification of dispersion effects in unreplicated experiments, is modified to be used in the context of split-plot experiments. The modification of the Bergman-Hynén method enables identification of factors that influence specific variance components in unreplicated two-level fractional factorial splitplot experiments. An industrial example is used to illustrate the proposed method.     

Characterizing and Approximating Infinite Scale Mixtures of Normals

ABSTRACT

The purpose of this study is to approximate and identify infinite scale mixtures of normals, SMN. A new method for approximating any infinite SMN with a known mixing measure by a finite SMN is presented. In the new method, the modulus of continuity of the normal family as a function of the scale is used to discretize the mixing measure. This method will be used to approximate univariate and multivariate SMN with mean 0. In the multivariate case, two different methods are used to approximate the infinite SMN. Several results related to SMN are proved and other known ones are presented. For example, SMN are characterized by their corresponding Laplace transforms.