Statistical analysis of masked data in a hybrid system based on copula theory under progressive hybrid censoring

This article considers the reliability analysis of a hybrid system with dependent components, which are linked by a copula function. Based on Type I progressive hybrid censored and masked system lifetime data, we drive some probability results for the hybrid system and then the maximum likelihood estimates as well as the asymptotic confidence intervals and bootstrap confidence intervals of the unknown parameters are obtained. The effects of different dependence structures on the estimates of the parameter and the reliability function are investigated. Finally, Monte Carlo simulations are implemented to compare the performances of the estimates when the components are dependent with those when the components are independent.     

COMPARISON OF TIME AND CROSS-SECTIONAL AGGREGATION UNDER A TIME SERIES RANDOM COMPONENT MODEL

Abstract. Small-area estimation under a stationary time series random component model is considered. Cross-sectional aggregation and varying degrees of time aggregation are treated as competing prediction methods. An estimated mean-squared prediction error criterion is used to compare these methods. Some exact and asymptotic properties of this criterion are developed, a consistent estimator of the associated asymptotic variance is presented and simultaneous approximate confidence intervals for the mean-squared prediction errors are discussed. Time aggregation of a single series is considered as a special case. In addition, an extension to the assessment of mean-squared prediction errors of synthetic small-area predictors is outlined.     

Current Status of Cell-Based Therapy in Patients with Critical Limb Ischemia

(1) Background: The treatment of peripheral arterial disease (PAD) is focused on improving perfusion and oxygenation in the affected limb. Standard revascularization methods include bypass surgery, endovascular interventional procedures, or hybrid revascularization. Cell-based therapy can be an alternative strategy for patients with no-option critical limb ischemia who are not eligible for endovascular or surgical procedures. (2) Aims: The aim of this narrative review was to provide an up-to-date critical overview of the knowledge and evidence-based medicine data on the position of cell therapy in the treatment of PAD. The current evidence on the cell-based therapy is summarized and future perspectives outlined, emphasizing the potential of exosomal cell-free approaches in patients with critical limb ischemia. (3) Methods: Cochrane and PubMed databases were searched for keywords “critical limb ischemia and cell therapy”. In total, 589 papers were identified, 11 of which were reviews and 11 were meta-analyses. These were used as the primary source of information, using cross-referencing for identification of additional papers. (4) Results: Meta-analyses focusing on cell therapy in PAD treatment confirm significantly greater odds of limb salvage in the first year after the cell therapy administration. Reported odds ratio estimates of preventing amputation being mostly in the region 1.6–3, although with a prolonged observation period, it seems that the odds ratio can grow even further. The odds of wound healing were at least two times higher when compared with the standard conservative therapy. Secondary endpoints of the available meta-analyses are also included in this review. Improvement of perfusion and oxygenation parameters in the affected limb, pain regression, and claudication interval prolongation are discussed. (5) Conclusions: The available evidence-based medicine data show that this technique is safe, associated with minimum complications or adverse events, and effective.     

Weighted Estimation of Harmonic Components in a Musical Sound Signal

The study of musical sound has become a popular research field. Harmonic regression signal plus noise statistical models have been used to analyze sound signals. However, it is common to give estimates of harmonic parameters without indications of their uncertainties. Least squares estimates for harmonic models have been studied and asymptotic variance expression have been developed. In practice, window-based estimates are used. This paper studies the statistical properties of such estimates; in particular, we use asymptotic variance expressions to develop standard errors and construct confidence intervals. We present applications and examples of the statistical techniques to musical sound signal analysis.     

Practical methods for competing risks data: a review

Competing risks data arise naturally in medical research, when subjects under study are at risk of more than one mutually exclusive event such as death from different causes. The competing risks framework also includes settings where different possible events are not mutually exclusive but the interest lies on the first occurring event. For example, in HIV studies where seropositive subjects are receiving highly active antiretroviral therapy (HAART), treatment interruption and switching to a new HAART regimen act as competing risks for the first major change in HAART. This article introduces competing risks data and critically reviews the widely used statistical methods for estimation and modelling of the basic (estimable) quantities of interest. We discuss the increasingly popular Fine and Gray model for subdistribution hazard of interest, which can be readily fitted using standard software under the assumption of administrative censoring. We present a simulation study, which explores the robustness of inference for the subdistribution hazard to the assumption of administrative censoring. This shows a range of scenarios within which the strictly incorrect assumption of administrative censoring has a relatively small effect on parameter estimates and confidence interval coverage. The methods are illustrated using data from HIV-1 seropositive patients from the collaborative multicentre study CASCADE (Concerted Action on SeroConversion to AIDS and Death in Europe).     

Evaluation of realistic 95% confidence intervals for the activation energy calculated by the iterative linear integral isoconversional method

Cai and Chen have proposed a new iterative linear integral isoconversional method that is capable of providing more accurate values of the activation energy than the traditional linear isoconversional methods (Cai, Junmeng, Chen, Siyu, 2009. Journal of Computational Chemistry 30, 1986–1991). However, an analysis of the estimation of confidence intervals for the activation energy determined by this iterative linear integral isoconversional method is still missing. Therefore, this short communication focuses on estimating realistic confidence intervals for the activation energy calculated by the isoconversional method. For this purpose, a comparison of confidence intervals estimated using the Vyazovkin–Sbirrazzuoli corrected Student's percentiles (Vyazovkin, Sergey, Sbirrazzuoli, Nicolas, 1997. Analytica Chimica Acta 355, 175–180) and a nonparametric method has indicated that the use of the Vyazovkin–Sbirrazzuoli method tends to overestimate confidence intervals for three heating rate estimates. The new corrected Student's percentiles for realistic 95% confidence intervals ?_n–2,0.975 of 2.9, 2.5 and 2.3 for three, four and five heating rate estimates, respectively, can be used to obtain realistic confidence intervals for the activation energy computed by the iterative linear integral isoconversional method.     

Proving non-inferiority or equivalence of two treatments with dichotomous endpoints using exact methods

Since the early work of RA Fisher, exact methods have been recognized as important tools in data analysis because they provide valid statistical inference even with small sample sizes, or with sparse or skewed data. With the recent advance of computational power and the availability of commercial software packages, exact methods have gained substantial popularity over the past two decades. However, most of these exact methods have been devoted to testing classical null hypotheses of no differences, and until recently little was known about exact methods dealing with non-inferiority or equivalence hypotheses. The presence of nuisance parameters in testing non-inferiority/equivalence hypotheses presents a special challenge for exact methods because of the intense computational requirement. In this paper, we review exact methods available for proving non-inferiority or equivalence of two treatments with a dichotomous endpoint. First, we present the general methodology for conducting exact tests for non-inferiority or equivalence; we then discuss several unconditional and conditional methods available for constructing hypothesis tests and confidence intervals based on three commonly used measures, namely, the difference, relative risk, and odds ratio of two independent proportions or rates. Finally, we illustrate with several examples the application of these exact methods in analysing and planning non-inferiority or equivalence trials.     

Comparison of methods to identify outliers observed in health services small area variation studies

Small area variation analysis (SAV) is an established methodology in health services and epidemiological research. The goal is to demonstrate that rates differ across areas, and to explain these differences by differences in physician practice styles or patient characteristics. While the SAV statistics provide an overall variation estimate, they do not provide a statistical means to identify significant outliers. We compared the chi-square (chi2) test with three approaches in determining significant outliers in SAV. We used data from the Canadian Institute for Health Information (CIHI) for Ontario residents discharged between 1989 and 1991. Coronary artery bypass surgery, hysterectomy and hip replacement data were used to compare four statistics in determining outliers: the chi2 test, Swift's approximate bootstrap confidence interval (ABC), Carriere's T2 (T2) with simultaneous confidence intervals (SCI), and Gentleman's normalized scores (GNS). Both the ABC and SCI correct the skewness of the distribution of the adjusted rates. With large data, confidence intervals calculated by the normal or the ABC methods are indistinguishable. The T2 can be applied to also nonbinary events. For binary events, it is asymptotically the same as the chi2. The GNS ranks the rates, but the distribution of these ranks does not differ significantly from that of the adjusted rates. We concluded that when using large data with binary events, there is little advantage in using the ABC, SCI or GNS over the commonly known chi2. The chi2 remains a useful tool in small area variation analysis to 'screen' or flag potential differences beyond chance alone.     

Bootstrapping confidence intervals for the change‐point of time series

Abstract. We study an at‐most‐one‐change time‐series model with an abrupt change in the mean and dependent errors that fulfil certain mixing conditions. We obtain confidence intervals for the unknown change‐point via bootstrapping methods. Precisely, we use a block bootstrap of the estimated centred error sequence. Then, we reconstruct a sequence with a change in the mean using the same estimators as before. The difference between the change‐point estimator of the resampled sequence and the one of the original sequence can be used as an approximation of the difference between the real change‐point and its estimator. This enables us to construct confidence intervals using the empirical distribution of the resampled time series. A simulation study shows that the resampled confidence intervals are usually closer to their target levels and at the same time smaller than the asymptotic intervals.     

污水处理厂出水水质变量区间预测建模

为了实现污水处理厂的有效运行，需要建立能够精确描述水厂行为的模型。根据水厂入水和出水数据，采用径向基函数神经网络建立污水处理过程模型。考虑到建模误差有界，使用参数线性集员辨识算法分别得到隐含层到输出层各神经元连接权值向量的不确定集合描述。与现有的单输出区间预测模型相比，该模型能够根据水厂入水数据同时给出多个出水水质变量的置信区间。这些区间能表征出水变量的存在范围，从而实现水质变量的可靠估计，进而评估出水水质或水厂性能。此外，还将此出水区间预测模型用于污水处理厂的故障检测与隔离，以提高水厂运行的可靠性。实验结果表明文中所提方法的有效性。     

A Comparison of the Kubelka-Munk Reflectance with the Exact Reflectance for Isotropic Scattering

The Kubelka-Munk reflectance is compared with the exact reflectance of an isotropically scattering material, under normal experimental conditions, by obtaining estimates of the accuracy of both methods in predicting the colour of mixtures of dyes on textiles. The exact analysis produces results that, on average, are 14% more accurate than those obtained with the Kubelka-Munk analysis.     

Statistical analysis of slow crack growth experiments

A common approach for the determination of slow crack growth (SCG) parameters are the static and dynamic loading method. Since materials with small Weibull module show a large variability in strength, a correct statistical analysis of the data is indispensable. In this work we propose the use of the Maximum Likelihood Method and a Baysian Analysis, which, in contrast to the standard procedures, take into account that failure strengths are Weibull distributed. The analysis provides estimates for the SCG parameters, the Weibull module, and the corresponding confidence intervals and overcomes the necessity of manual differentiation between inert and fatigue strength data. We compare the methods to a Least Squares approach, which can be considered the standard procedure. The results for dynamic loading data from the glass sealing of MEMS devices show that the assumptions inherent to the standard approach lead to significantly different estimates.     

ASYMPTOTIC SIMULTANEOUS CONFIDENCE BANDS FOR AUTOREGRESSIVE SPECTRAL DENSITY

Abstract. On the basis of the asymptotic behaviour of autoregressive parameter estimates, the properties of autoregressive spectral density estimates are deduced. The simultaneous confidence bands for the spectra are derived using Šidák's inequality. Simulation experiments are used to illustrate the quality of the derived confidence bands.     

Maximum‐likelihood maximum‐entropy constrained probability density function estimation for prediction of rare events

This work addresses the problem of estimating complete probability density functions (PDFs) from historical process data that are incomplete (lack information on rare events), in the framework of Bayesian networks. In particular, this article presents a method of estimating the probabilities of events for which historical process data have no record. The rare‐event prediction problem becomes more difficult and interesting, when an accurate first‐principles model of the process is not available. To address this problem, a novel method of estimating complete multivariate PDFs is proposed. This method uses the maximum entropy and maximum likelihood principles. It is tested on mathematical and process examples, and the application and satisfactory performance of the method in risk assessment and fault detection are shown. Also, the proposed method is compared with a few copula methods and a nonparametric kernel method, in terms of performance, flexibility, interpretability, and rate of convergence. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1013–1026, 2014     

中、小型水溶液全循环法尿素装置特大安全事故隐患和有效防范(上)

尿素装置工艺过程存在着爆炸三要素,发生过多次特大爆炸事故,损失惨重,文中详细地分析了事故隐患范围和原因以及现有防范措施的使用局限性,作者提出的脱H2工艺新技术是从源头上有效地防范爆炸事故的发生,是“安全生产”和“放心操作”的有力保障。     

中、小型水溶液全循环法尿素装置特大安全事故隐患和有效防范(下)

尿素装置工艺过程存在着爆炸三要素,发生过多次特大爆炸事故,损失惨重。文中详细地分析了事故隐患范围和原因以及现有防范措施的使用局限性;作者提出了脱H2工艺新技术是从头源头上有效地防范爆炸事故的发生,是“安全生产”和“放心操作”的有力保障。     

Assessing Time‐Reversibility Under Minimal Assumptions

Abstract. This article considers a simple procedure for assessing whether a weakly dependent univariate stochastic process is time‐reversible. Our approach is based on a simple index of the deviation from zero of the median of the one‐dimensional marginal law of differenced data. An attractive feature of the method is that it requires no moment assumptions. Instead of relying on Gaussian asymptotic approximations, we consider using subsampling and resampling methods to construct confidence intervals for the time‐reversibility parameter, and show that such inference procedures are asymptotically valid under a mild mixing condition. The small‐sample properties of the proposed procedures are examined by means of Monte Carlo experiments and an application to real‐world data is also presented.     

Dealing with discreteness: making 'exact' confidence intervals for proportions,differences of proportions,and odds ratios more exact

'Exact' methods for categorical data are exact in terms of using probability distributions that do not depend on unknown parameters. However, they are conservative inferentially. The actual error probabilities for tests and confidence intervals are bounded above by the nominal level. This article examines the conservatism for interval estimation and describes ways of reducing it. We illustrate for confidence intervals for several basic parameters, including the binomial parameter, the difference between two binomial parameters for independent samples, and the odds ratio and relative risk. Less conservative behavior results from devices such as (1) inverting tests using statistics that are 'less discrete', (2) inverting a single two-sided test rather than two separate one-sided tests each having size at least half the nominal level, (3) using unconditional rather than conditional methods (where appropriate) and (4) inverting tests using alternative p-values. The article concludes with recommendations for selecting an interval in three situations-when one needs to guarantee a lower bound on a coverage probability, when it is sufficient to have actual coverage probability near the nominal level, and when teaching in a classroom or consulting environment.     

Estimating the Mean Direction of Strongly Dependent Circular Time Series

A class of circular processes based on Gaussian subordination is introduced. This allows for flexible modelling of directional time series with long-range dependence. Based on limit theorems for subordinated processes and consistent estimation of nuisance parameters, asymptotic confidence intervals for the mean direction are derived. Extensions to cases where the direction depends on explanatory variables are also considered. Simulations and a data example illustrate the proposed method.