A model for k-out-of-m load-sharing systems

ABSTRACT

In a load-sharing system, the failure of a component affects the residual lifetime of the surviving components. We propose a model for the load-sharing phenomenon in k-out-of-m systems. The model is based on exponentiated conditional distributions of the order statistics formed by the failure times of the components. For an illustration, we consider two component parallel systems with the initial lifetimes of the components having Weibull and linear failure rate distributions. We analyze one data set to show that the proposed model may be a better fit than the model based on sequential order statistics.     

Deviance residuals in generalised log-gamma regression models with censored observations

In this article, we compare three residuals based on the deviance component in generalised log-gamma regression models with censored observations. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. For all cases studied, the empirical distributions of the proposed residuals are in general symmetric around zero, but only a martingale-type residual presented negligible kurtosis for the majority of the cases studied. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for the martingale-type residual in generalised log-gamma regression models with censored data. A lifetime data set is analysed under log-gamma regression models and a model checking based on the martingale-type residual is performed.     

A bivariate regression model for matched paired survival data: local influence and residual analysis

The use of bivariate distributions plays a fundamental role in survival and reliability studies. In this paper, we consider a location scale model for bivariate survival times based on the proposal of a copula to model the dependence of bivariate survival data. For the proposed model, we consider inferential procedures based on maximum likelihood. Gains in efficiency from bivariate models are also examined in the censored data setting. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the bivariate regression model for matched paired survival data. Sensitivity analysis methods such as local and total influence are presented and derived under three perturbation schemes. The martingale marginal and the deviance marginal residual measures are used to check the adequacy of the model. Furthermore, we propose a new measure which we call modified deviance component residual. The methodology in the paper is illustrated on a lifetime data set for kidney patients.     

Statistical inference for restricted partially linear varying coefficient errors-in-variables models

As a useful extension of partially linear models and varying coefficient models, the partially linear varying coefficient model is useful in statistical modelling. This paper considers statistical inference for the semiparametric model when the covariates in the linear part are measured with additive error and some additional linear restrictions on the parametric component are available. We propose a restricted modified profile least-squares estimator for the parametric component, and prove the asymptotic normality of the proposed estimator. To test hypotheses on the parametric component, we propose a test statistic based on the difference between the corrected residual sums of squares under the null and alterative hypotheses, and show that its limiting distribution is a weighted sum of independent chi-square distributions. We also develop an adjusted test statistic, which has an asymptotically standard chi-squared distribution. Some simulation studies are conducted to illustrate our approaches.     

SURVIVAL ANALYSIS WITH TIME DEPENDENT FRAILTY USING A LONGITUDINAL MODEL

A method of estimation for generalised mixed models is applied to the estimation of regression parameters in a proportional hazards model with time dependent frailty. A parameter representing change over time is introduced and is modelled in turn into a fixed effect, a normally distributed random effect and a longitudinal effect in which the random component relates to the patient characteristics. Both maximum likelihood and residual maximum likelihood estimators are given.     

The specification of vector autoregressive moving average models

In this paper we propose a new identification method based on the residual white noise autoregressive criterion (Pukkila et al., 1990) to select the order of VARMA structures. Results from extensive simulation experiments based on different model structures with varying number of observations and number of component series are used to demonstrate the performance of this new procedure. We also use economic and business data to compare the model structures selected by this order selection method with those identified in other published studies.     

Editorial collaborators

A simulation study of the binomial-logit model with correlated random effects is carried out based on the generalized linear mixed model (GLMM) methodology. Simulated data with various numbers of regression parameters and different values of the variance component are considered. The performance of approximate maximum likelihood (ML) and residual maximum likelihood (REML) estimators is evaluated. For a range of true parameter values, we report the average biases of estimators, the standard error of the average bias and the standard error of estimates over the simulations. In general, in terms of bias, the two methods do not show significant differences in estimating regression parameters. The REML estimation method is slightly better in reducing the bias of variance component estimates.     

Deviance Residuals for an Angular Response

This paper discusses deviance residual approximations in von Mises regression models. By using a relationship between the von Mises and the wrapped normal distributions, the paper shows that the deviance component of the von Mises distribution is approximately a linear function of the standard normal distribution. Two standardized forms are proposed for the deviance residual, and a simulation study is performed to compare the approximation of the proposed residuals to the standard normal distribution. An illustrative example is given.     

Functional principal component analysis in age–period–cohort analysis of body mass index data by gender and ethnicity

In this paper, we propose a two-stage functional principal component analysis method in age–period–cohort (APC) analysis. The first stage of the method considers the age–period effect with the fitted values treated as an offset; and the second stage of the method considers the residual age–cohort effect conditional on the already estimated age-period effect. An APC version of the model in functional data analysis provides an improved fit to the data, especially when the data are sparse and irregularly spaced. We demonstrate the effectiveness of the proposed method using body mass index data stratified by gender and ethnicity.     

Trend and seasonal decomposition in discrete time

A time series is decomposed into a trend-cyclical plus seasonal component by minimizing the sum of a smoothness and a goodness of fit criterion. The smoothness criterion is such that polynomials (trend-cyclical component) and trigonometric functions (seasonal component) are rated with the ideal value zero. The residual sum of squares serves as goodness of fit criterion. The solution is then decomposed into the two components in a natural way.     

A graphical model selection tool for mixed models

ABSTRACT

Model selection can be defined as the task of estimating the performance of different models in order to choose the most parsimonious one, among a potentially very large set of candidate statistical models. We propose a graphical representation to be considered as an extension to the class of mixed models of the deviance plot proposed in the literature within the framework of classical and generalized linear models. This graphical representation allows, once a reduced number of models have been selected, to identify important covariates focusing only on the fixed effects component, assuming the random part properly specified. Nevertheless, we suggest also a standalone figure representing the residual random variance ratio: a cross-evaluation of the two graphical representations will allow to derive some conclusions on the random part specification of the model and a more accurate selection of the final model.     

An Additive–Multiplicative Restricted Mean Residual Life Model

The mean residual life measures the expected remaining life of a subject who has survived up to a particular time. When survival time distribution is highly skewed or heavy tailed, the restricted mean residual life must be considered. In this paper, we propose an additive–multiplicative restricted mean residual life model to study the association between the restricted mean residual life function and potential regression covariates in the presence of right censoring. This model extends the proportional mean residual life model using an additive model as its covariate dependent baseline. For the suggested model, some covariate effects are allowed to be time‐varying. To estimate the model parameters, martingale estimating equations are developed, and the large sample properties of the resulting estimators are established. In addition, to assess the adequacy of the model, we investigate a goodness of fit test that is asymptotically justified. The proposed methodology is evaluated via simulation studies and further applied to a kidney cancer data set collected from a clinical trial.     

A note on the mean residual life of a coherent system with a cold standby component

In this paper, we investigate the effect of a cold standby component on the mean residual life (MRL) of a system. When the system fails, a cold standby component is immediately put in operation. We particularly focus on the coherent systems in which, after putting the standby component into operation, the failure of the system is due to the next component failure. For these systems, we define MRL functions and obtain their explicit expressions. Also some stochastic ordering results are provided. Such systems include k-out-of-n systems. Hence, our results extend some results in literature.     

Semiparametric median residual life model and inference

For randomly censored data, the authors propose a general class of semiparametric median residual life models. They incorporate covariates in a generalized linear form while leaving the baseline median residual life function completely unspecified. Despite the non‐identifiability of the survival function for a given median residual life function, a simple and natural procedure is proposed to estimate the regression parameters and the baseline median residual life function. The authors derive the asymptotic properties for the estimators, and demonstrate the numerical performance of the proposed method through simulation studies. The median residual life model can be easily generalized to model other quantiles, and the estimation method can also be applied to the mean residual life model. The Canadian Journal of Statistics 38: 665–679; 2010 © 2010 Statistical Society of Canada     

Estimation of surgeon effects in the analysis of post-operative colorectal cancer patients data

There has been increasing interest in the assessment of surgeon effects for survival data of post-operative cancer patients. In particular, the measurement of surgeon's surgical performance after eliminating significant risk variables is considered. The generalized linear mixed model approach, which assumes a log-normal-distributed surgeon effects in the hazard function, is adopted to assess the random surgeon effects of post-operative colorectal cancer patients data. The method extends the traditional Cox's proportional hazards regression model, by including a random component in the linear predictor. Estimation is accomplished by constructing an appropriate log-likelihood function in the spirit of the best linear unbiased predictor method and extends to obtain residual maximum likelihood estimates. As a result of the non-proportionality of the hazard of colon and rectal cancer, the data are analyzed separately according to these two kinds of cancer. Significant risk variables are identified. The 'predictions' of random surgeon effects are obtained and their association with the rank of surgeon is examined.     

On the design of optimal change-over experiments through multi-objective simulated annealing

The construction of optimal designs for change-over experiments requires consideration of the two component treatment designs: one for the direct treatments and the other for the residual (carry-over) treatments. A multi-objective approach is introduced using simulated annealing, which simultaneously optimises each of the component treatment designs to produce a set of dominant designs in one run of the algorithm. The algorithm is used to demonstrate that a wide variety of change-over designs can be generated quickly on a desk top computer. These are generally better than those previously recorded in the literature.     

Testing for the parametric component of partially linear EV models under random censorship

This paper investigates the hypothesis test of the parametric component in partially linear errors-in-variables (EV) model with random censorship. We construct two test statistics based on the difference of the corrected residual sum of squares and empirical likelihood ratio under the null and alternative hypotheses. It is shown that the limiting distributions of the proposed test statistics are both weighted sum of independent standard chi-squared distribution with one degree of freedom under the null hypothesis. Based on the adjusted test statistics, we further develop two new types of test procedures. Finite sample performance of the proposed test procedures is evaluated by extensive simulation studies.     

Testing residual normality in the ANOVA model

The use of single group skewness and kurtosis critical values for the assessment of residual normality in the ANOVA model is examined. Using single group critical values gives a conservative test of residual normality in multiple group designs. As the sample size per group increases, the empirical Type I error rates for the skewness and kurtosis tests of residual normality approach a. These results supplement previous work which has focused on testing residual normality in the linear regression model.     

Residual analysis for parametric models fit to censored data

The focus of this paper is on residual analysis for the lognormal and extreme value or Weibull models, although the proposed methods can be applied to any parametric model. Residuals developed by Barlow and Prentice (1988) for the Cox proportional hazards model are extended to the parametric model setting. Three different residuals are proposed based on this approach with two residuals measuring the impact of survival time and one measuring the impact of the covariates included in the model. In addition, a residual derived from the deviations equality presented in Efron and Johnstone (1990) and the residual proposed by Joergensen (1984) for censored data models are discussed.     

空气质量指数监控与预测的控制图方法

世界上多数国家都采用空气质量指数这一指标衡量空气质量状况,对空气质量的有效监测和预警是解决空气污染的重要参考依据.本研究使用ARMA模型拟合空气污染指数(API)时序数据,通过模型残差建立控制图,根据控制图的变化监控并预警.研究采用2010年上海世博会API作为可控状态建立控制限,以2011年1～8月上海API数据建立ARMA(1,1)模型,通过2011年9月上海API模型预测与残差控制图证实模型和控制图的有效性.