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The two-parameter Rayleigh distribution, as an extended distribution of the Rayleigh distribution, has been widely applied in reliability analysis. With the introduction of the location parameter, two-parameter Rayleigh distribution becomes more flexible in fitting real-data. In this paper, based on generalized progressively hybrid censored(GPHC) sample from the two-parameter Rayleigh distribution, Classical and Bayesian inferences are discussed. The Newton-Raphson(NR) and Expectation-Maximization(EM) algorithms are used to compute the maximum likelihood estimates(MLEs). As well as the asymptotic confidence interval(ACI) estimation is obtained through the asymptotic distribution theory of maximum likelihood estimation(MLE) and computation of the observed Fisher information matrix. In Bayesian frame, the estimation of unknown parameters and prediction of future observable are taken into consideration. Due to Bayesian estimation is challenging to compute precisely and for the purpose of comparison, the Lindley's approximation, the Tierney-Kadane(TK) approximation and Markov chain Monte Carlo(MCMC) method are employed to obtain Bayesian estimates. Then, combining the MCMC algorithm mentioned in the article, the one- and two- samples Bayesian prediction are obtained. Finally, the simulation results are provided and a real-life data set is used for illustration purpose. [ABSTRACT FROM AUTHOR]

In this paper, statistical inference of an inverted exponentiated Rayleigh model is studied when the failure times are obtained under a modified progressive hybrid censoring. The maximum likelihood estimators of the model parameters together with associated existence and uniqueness are established, and approximate confidence intervals are constructed based on asymptotic theory. Alternatively, generalized point and interval estimates for unknown parameters are also constructed based on the proposed pivotal quantities for comparison. In addition, predictive intervals of remaining useful life from the inverted exponentiated Rayleigh distribution are also constructed under classical and generalized inferential approaches, respectively. Finally, extensive simulation studies are carried out to compare the performance of the proposed methods, and two real-life examples are analyzed for illustration. The numerical results indicate that both traditional likelihood and generalized inferential methods work satisfactorily, and that our proposed generalized approach appears much more appealing and are superior to classical results. [ABSTRACT FROM AUTHOR]

In this paper, estimation and prediction inference of power Muth distribution, with the progressive censoring data, are described. The maximum likelihood and Bayesian approaches of the unknown parameters are considered. Several Bayesian estimators are obtained against different symmetric and asymmetric loss functions, such as squared error, linex and general entropy. Also, the asymptotic confidence intervals and highest posterior density credible intervals of them are derived. Most focus of this paper is Bayesian prediction of the removed units in multiple stages of the progressively censored sample, so that, the Gibbs and Metropolis samplers are used, to reach this end. To compare the performance of different methods, Mont Carlo simulation is employed. Moreover, one practical data set is analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

Competing risks data frequently appear in real-world operations like quality inspections, survival analysis, reliability tests, and clinical trials. From the quality point of view, relative risk rate can be considered an interesting quality indicator in analyzing the competing risks data for statistical process monitoring purposes. The relative risk rate measures the proportion of failures caused by the primary risk among a set of competing risks. This paper introduces two Shewhart-type control charts for monitoring the relative risk rate when the lifetimes of competing risks are independent Weibull random variables. The former chart is constructed based on the maximum likelihood estimation method, while the latter is developed based on the Bayesian approach. The proposed control charts can be applied in Phase II. The calculation of the Bayesian control charts and the evaluation of both process monitoring techniques have been done based on Monte Carlo simulations. The performance of the proposed control charts has been examined based on the average run length metric. The illustrative example is also discussed in detail to demonstrate the applicability of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the stress-strength reliability estimation under balanced joint Type-II progressive censoring scheme for independent samples from two different populations. We simultaneously place two independent samples where the experimental units follow Weibull distributions with common shape parameter β and different scale parameters α, λ, respectively. The maximum likelihood estimators of the unknown parameters are derived. Further, the Bayesian inference is considered using Lindley's approximation and Gibbs sampling method. Extensive simulations are performed to see the effectiveness of the proposed estimation methods. Further, we derive the optimal censoring scheme in the Bayesian framework by using the variable neighbourhood search method proposed by [Bhattacharya et al. On optimum life-testing plans under type-ii progressive censoring scheme using variable neighbourhood search algorithm. Test. 2016;25(2):309–330]. Further, some simulation schemes are provided to compare the performances of the estimations under the jointly censored samples versus two separate censored samples. [ABSTRACT FROM AUTHOR]

In this paper we extend the family of test proposed by Majumder and Mitra [Detecting trend change in failure functions-an L-statistic approach. Stat Pap. 2019;62:31–52. doi: ] for testing exponentiality against bathtub (BT) failure rate (upside down bathtub (UBT)) to randomly right censored case. We derive the asymptotic distribution of the test statistic and using Monte Carlo simulation we obtain the empirical powers for certain alternative distributions. As a special case the asymptotic distribution of the test statistic proposed by Park [Testing whether failure rate changes its trend. IEEE Trans Reliab. 1988;37(4):375–378. doi: ] is obtained. Finally some examples of real life data are given for illustrative purpose. [ABSTRACT FROM AUTHOR]

PAST WINNERS OF TECHNOMETRICS PRIZES (1969-2020) B Jack Youden Prize for Best Expository Paper b 2020 I Daniel J. Eck, Christopher J. Nachtsheim, Thomas A. Albrecht, and R. Dennis Cook i - Multivariate Design of Experiments for Engineering Dimensional Analysis 2019 I Mickael Binois, Jiangeng Huang, Robert Gramacy, and Mike Ludkovski i for the article Replication or Exploration? The 2021 Frank Wilcoxon Prize for Best Practical Application Paper was awarded to I Jakob Raymaekers and Peter J. Rousseeuw i for the article B "Fast Robust Correlation for High-Dimensional Data," b DOI: 10.1080/00401706.2019.1677270. The 2021 Jack Youden Prize for Best Expository Paper was awarded to I Xueqi Zhao and Enrique del Castillo i for their article B "An Intrinsic Geometrical Approach for Statistical Process Control of Surface and Manifold Data," b DOI: 10.1080/00401706.2020.1772114. [Extracted from the article]

This article considers the Bayes analysis of generalized gamma accelerated failure time model and its two components Weibull and gamma when the given observations are left truncated and right censored. In order to perform the analysis, the paper proposes the use of an improved version of the Metropolis-Hastings algorithm, namely, the Metropolis-adjusted Langevin algorithm. Besides, the paper also checks the model compatibility and compares the considered models with its components using the Bayes factor computed on the basis of a recent methodology. A numerical illustration is provided based on a simulated as well as a real dataset. The real dataset consists of individuals infected with human immunodeficiency virus who are at the risk of acquired immunodeficiency syndrome and subsequent deaths. The numerical illustration is further extended to check the effect of different therapies including the highly active antiretroviral therapy on the lifetime of individuals. [ABSTRACT FROM AUTHOR]

Shelf life of a food product is a time threshold that determines when it no longer retains its quality. It can be estimated using data coming from sensory experiments where potential consumers taste aged portions of the product and state whether they will consume the product or not. The raw data obtained from the experiment consist of a binary sequence for each assessor. The standard approach to analyze this type of data is based on reliability theory and requires the coding of the raw data into censored intervals. This paper discusses how the aforementioned coding yields a loss of information and low coverage of confidence intervals. Furthermore, the paper introduces an alternative methodology to estimate shelf life based on longitudinal data theory. This methodology prevents loss of information, quantifies the effect of inconsistent responses, explicitly incorporates and diagnoses the correlation structure of the consumer's responses, and provides an easier interpretation of the results for the final user. These features are shown using real data coming from sensory experiments. [ABSTRACT FROM AUTHOR]

This paper considers inference on the partial area under the receiver operating characteristic curve based on two independent progressively Type-II censored samples from the populations that are belonging to the lower truncated proportional hazard rate models with the same baseline distributions. The maximum likelihood estimator, a generalized pivotal estimator and some Bayes estimators are obtained for three structures of prior distributions. The percentile bootstrap confidence interval, a generalized pivotal confidence interval and some Bayesian credible intervals are also presented. A Monte-Carlo simulation study is used to evaluate the performances of the obtained point estimators and confidence and credible intervals. Finally, a real data set is applied for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, a unit inverse Weibull distribution as well as its basic structural properties is proposed. Furthermore, classical inferences for multicomponent reliability are discussed under type-II censoring when stress and strength components have a common parameter. The maximum likelihood estimator of the reliability is obtained and in sequel an asymptotic interval is constructed. Pivotal quantities are constructed and then generalized point and interval estimators are obtained for the reliability. Likelihood and pivotal quantities-based estimations are presented when all parameters are unequal as well. The performance of different estimators is investigated using simulation studies and real-life examples are studied from an application viewpoint. Finally, some concluding remarks are given. [ABSTRACT FROM AUTHOR]

Two-parameter exponential distributions have a widespread application in insurance, medical and industrial production. However, incomplete samples are often obtained due to experimental conditions. In this paper, a new adaptive exponentially weighted moving average control chart, called AEWMA-LR control chart, is proposed for monitoring the quality characteristics of two-parameter exponential distributions based on type-II censored data. The proposed monitoring scheme aims to achieve an adaptive effect by combining exponentially weighted moving averages and adjusting the weight factors according to the relative magnitude of the estimated location and scale parameter shifts. We explored the effects of smooth parameters, sample size, and censored parameters on the performance of AEWMA-LR control charts through a Monte Carlo simulation study. Then, a comparative analysis was conducted with existing EWMA-LR and EWMA-Max-MLE control charts based on the two-parameter exponential model. The simulation results of zero-state average run length (ARL) and conditional expected delay (CED) show that the proposed monitoring scheme outperforms the existing control charts. Finally, to demonstrate the usefulness of the AEWMA-LR control chart in real-world applications, we give three instances of two-parameter exponential distributions based on type-II right censored data. [ABSTRACT FROM AUTHOR]

In this paper, statistical inferences for the parameters, reliability, and failure rate functions (as parameters) of the exponentiated Kies distribution are accomplished using maximum likelihood and both Lindley and Markov chain Monte Carlo techniques, under adaptive Type-II progressive censoring. Depending on the Fisher information matrix and the delta method, we find the approximate confidence intervals for the parameters and the reliability and failure rate functions, respectively. Furthermore, the samples generated from Markov chains Monte Carlo are used to generate credible intervals for the parameters, reliability, and failure rates functions. Symmetric and asymmetric loss functions are also used to find Bayes estimators using Markov chain Monte Carlo and Lindley techniques. Comparisons between the two techniques of evaluation for different estimators under different sizes of data sets are conducted. Finally, a real-life example is applied to clarify the results of the used techniques. [ABSTRACT FROM AUTHOR]

It has attracted a great deal of interest in randomized survival studies to assess the causal treatment effect under non-compliance with time-to-event outcomes. In this paper, the problem when one faces case–cohort studies for which covariates are usually too expensive to be measured or obtained for the full cohort and also the disease rate is generally low is considered. Furthermore, only interval-censored data may be available for the failure event of interest, a situation for which there does not seem to exist an established estimation procedure. To address the problem, a sieve inverse probability weighting estimation procedure is proposed, and the resulting estimators are shown to be consistent and asymptotically normal. A simulation study is conducted to evaluate the finite sample performance of the proposed approach and suggests that it works well in practice. In addition, the method is applied to a breast cancer screening study. [ABSTRACT FROM AUTHOR]

In this paper, interval estimation of the two-parameter exponential distribution based on constant-stress accelerated life test data under Type-II censoring is studied. The life-stress models of the scale and location parameters are assumed to be log-linear. The maximum likelihood estimators of the model parameters are obtained. The exact and approximate confidence intervals for the parameters in the life-stress model of the scale parameter are developed. The generalized confidence intervals for the parameters in the life-stress model of the location parameter, and mean and reliability function at the designed stress level are derived. The performance of the proposed generalized confidence intervals is assessed by the Monte Carlo simulation. Finally, a real example is used to illustrate our methods. [ABSTRACT FROM AUTHOR]

In this paper, we study the robust estimation and empirical likelihood for the regression parameter in generalized linear models with right censored data. A robust estimating equation is proposed to estimate the regression parameter, and the resulting estimator has consistent and asymptotic normality. A bias-corrected empirical log-likelihood ratio statistic of the regression parameter is constructed, and it is shown that the statistic converges weakly to a standard $ \chi ^2 $ χ 2 distribution. The result can be directly used to construct the confidence region of regression parameter. We use the bias correction method to directly calibrate the empirical log-likelihood ratio, which does not need to be multiplied by an adjustment factor. We also propose a method for selecting the tuning parameters in the loss function. Simulation studies show that the estimator of the regression parameter is robust and the bias-corrected empirical likelihood is better than the normal approximation method. An example of a real dataset from Alzheimer's disease studies shows that the proposed method can be applied in practical problems. [ABSTRACT FROM AUTHOR]

The exponential distribution can provide a simple and appealing survival-time model in reliability analysis and life tests. Due to certain experimental designs, time limitations, budgetary requirements, and other reasons, however, only censored data can be obtained. In this paper, we propose a novel estimation procedure for the mean survival time of an exponential distribution under a sequential censoring scheme, which can be treated as a combination of type I censoring and type II censoring. The procedure makes a trade-off between estimation error and sampling cost, using the minimum number of observations. An extensive set of Monte Carlo simulations is conducted to further validate its remarkable performance. To demonstrate the practical applicability, we then implement this newly proposed procedure to assess the reliability of various Backblaze's hard disk models. [ABSTRACT FROM AUTHOR]

AbstractWhen analyzing lifetime data in the presence of censoring one is often required to estimate the distribution function of the lifetimes non-parametrically. The most popular estimator used for this purpose is the Kaplan-Meier estimator. Interestingly, in its initial formulation this estimator is only defined up to the observed sample maximum. For values larger than the sample maximum two different assumptions are commonly used in the statistical literature. The first is to set the value of the estimate to one while the second is to use the value of the estimate at the sample maximum when estimating the tail of the distribution function. This paper illustrates the profound effect of these assumptions on the sizes and powers of goodness-of-fit tests for three classes of distributions often used in survival analysis. These differences are illustrated using observed remission time data. The considered classes of distributions are the exponential, Weibull and gamma. As a result of independent interest, we amend two classes of tests developed for the gamma distribution in the full sample case for use with censored data. [ABSTRACT FROM AUTHOR]

In recent years, some interested data can be recorded only if the values fall within an interval range, and the responses are often subject to censoring. Attempting to perform effective statistical analysis with censored, especially heavy-tailed and asymmetric data, can be difficult. In this paper, we develop a novel linear regression model based on the proposed skewed generalized t distribution for censored data. The likelihood-based inference and diagnostic analysis are established using the Expectation/Conditional Maximization Either algorithm in conjunction with smoothing approximate functions. We derive relevant measures to perform global influence for this novel model and develop local influence analysis based on the conditional expectation of the complete-data log-likelihood function. Some useful perturbation schemes are discussed. We illustrate the finite sample performance and the robustness of the proposed method by simulation studies. The proposed model is compared with other procedures based on a real dataset, and a sensitivity analysis is also conducted. [ABSTRACT FROM AUTHOR]

In this paper, we review some existing methods for testing goodness-of-fit based on progressively type-II censored samples in the location-scale family of distributions. Also, some similar procedures and new modifications are proposed. Using Monte Carlo simulation, the powers of the reviewed and proposed tests are compared for the normal and Gumbel distributions against several alternatives. Then, we present some results based on the simulation studies. Finally, an application to two datasets is presented for numerical illustration. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for analyzing bivariate positive data, taking into account a covariate vector and left-censored observations, by introducing a hierarchical Bayesian analysis. The proposed method assumes marginal Weibull distributions and employs either a usual Weibull likelihood or Weibull–Tobit likelihood approaches. A latent variable or frailty is included in the model to capture the possible correlation between the bivariate responses for the same sampling unit. The posterior summaries of interest are obtained through Markov Chain Monte Carlo methods. To demonstrate the effectiveness of the proposed methodology, we apply it to a bivariate data set from stellar astronomy that includes left-censored observations and covariates. Our results indicate that the new bivariate model approach, which incorporates the latent factor to capture the potential dependence between the two responses of interest, produces accurate inference results. We also compare the two models using the different likelihood approaches (Weibull or Weibull–Tobit likelihoods) in the application. Overall, our findings suggest that the proposed hierarchical Bayesian analysis is a promising approach for analyzing bivariate positive data with left-censored observations and covariate information. [ABSTRACT FROM AUTHOR]

This paper presents an effort to investigate the estimations of the Weibull distribution using an improved adaptive Type-II progressive censoring scheme. This scheme effectively guarantees that the experimental time will not exceed a pre-fixed time. The point and interval estimations using two classical estimation methods, namely maximum likelihood and maximum product of spacing, are considered to estimate the unknown parameters as well as the reliability and hazard rate functions. The approximate confidence intervals of these quantities are obtained based on the asymptotic normality of the maximum likelihood and maximum product of spacing methods. The Bayesian estimations are also considered using MCMC techniques based on the two classical approaches. An extensive simulation study is implemented to compare the performance of the different methods. Further, we propose the use of various optimality criteria to find the optimal sampling scheme. Finally, one real data set is applied to show how the proposed estimators and the optimality criteria work in real-life scenarios. The numerical outcomes demonstrated that the Bayesian estimates using the likelihood and product of spacing functions performed better than the classical estimates. [ABSTRACT FROM AUTHOR]

In this paper, a linear Bayes method is employed to simultaneously estimate the location parameter and the scale parameter of the extreme value distribution. Based on type II censored samples, we construct the linear Bayes estimator (LBE) of the parameter vector and establish its superiority over the classical unbiased estimator in terms of the mean square error matrix criterion. The proposed LBE is easy to calculate, and numerical results are presented to verify that the LBE works well. The estimator is further applied to a real data case to demonstrate its feasibility. [ABSTRACT FROM AUTHOR]

The analysis of left truncated and right censored data is very common in survival and reliability analysis. In lifetime studies patients are often subject to left truncation in addition to right censoring. For example, in bone marrow transplant studies based on International Bone Marrow Transplant Registry (IBMTR), the patients who die while waiting for the transplants will not be reported to the IBMTR. In this paper, we develop novel U-statistics under left truncation and right censoring. We prove the n -consistency of the proposed U-statistics. We derive the asymptotic distribution of the U-statistics using the counting process technique. As an application of the U-statistics, we develop a simple non-parametric test for testing the independence between time to failure and cause of failure in competing risks when the observations are subject to left truncation and right censoring. The finite sample performance of the proposed test is evaluated through a Monte Carlo simulation study. Finally, we illustrate our test procedure using the lifetime data of transformers. [ABSTRACT FROM AUTHOR]

The hazard rate function plays an important role in survival analysis. Extensive work has been carried out for building the point estimation of hazard rate function but limited work has been done for constructing its confidence bands, which is a fundamental issue in statistical inference. To fill in this gap, we focus on investigating this problem for right censored survival data in this paper. We first propose a debiased estimation for hazard rate function, based on which, we further construct the pointwise and simultaneous confidence bands for hazard rate function. We establish some theoretical properties of the proposed method, including the convergence rate and asymptotic distributions. The finite-sample performance of the proposed procedure is evaluated via both simulation studies and an application to a real data from the breast cancer study. [ABSTRACT FROM AUTHOR]

A single-parameter Pareto model, Pareto I, arises in many areas of application such as pricing of insurance risks, measuring income or wealth inequality in economics, or modelling lengths of telephone calls in telecommunications. In insurance, for example, it is common to work with data that are truncated (due to deductibles), censored (due to policy limits), and contaminated by outliers (due to model misspecification). Therefore, it is prudent to estimate Pareto I using robust procedures that are designed for such data transformations and are resistant to outliers. In this paper, we consider trimmed (T) and winsorized (W) estimators for the Pareto tail index α, and conduct a simulation study to check these estimators' performance in finite samples. Two broad aspects are investigated: Convergence of α ˆ 's to α as sample size increases from n = 25 to n = 1000. This is evaluated by presenting a series of boxplots and measuring each estimator's relative bias and finite-sample relative efficiency (with respect to the asymptotic variance of the maximum likelihood estimator, MLE). Sensitivity of α ˆ 's and of two value-at-risk estimates to a new observation (an outlier) that is placed at various locations within the sample ranging from the point of left-truncation/-censoring to the point of right-censoring. We find that with respect to (a), T- and W-estimators perform best when n is small and MLE outperforms its competitors when n is large. And with respect to (b), MLE is not robust whilst T's and W's can offer any desired degree of robustness. [ABSTRACT FROM AUTHOR]

Comparative lifetime experiments are of particular importance in production processes when one wishes to determine the relative merits of several competing products with regard to their reliability. This paper confines itself to the data obtained by running a joint progressive Type-II censoring plan on samples in a combined manner. The problem of Bayesian predicting failure times of surviving units is discussed in details when parent populations are exponential. Two real data sets are analyzed in order to illustrate all the inferential procedures developed here. When destructive experiments under a censoring scheme finished, the researchers are usually interested to estimate remaining lifetimes of surviving units for sequel experiments. Findings of this paper are useful for these purposes specially when samples are non-homogeneous such as those taken from industrial storages. [ABSTRACT FROM AUTHOR]

The selection of an appropriate life test plan is extremely important for any product as it not just improves the quality of the product but also reduces testing costs. In this approach, however, the choice of suitable costs play an important role. In this paper, a decision model is developed to determine the optimal life testing plan (LTP) by minimising the relevant costs involved for non-repairable products sold under the general rebate warranty. LTP are developed in the presence of Type-I hybrid censoring for products having Weibull distributed lifetimes. A constrained optimisation approach is followed considering both producer's and consumer's risk and suitable analysis techniques are employed in obtaining the optimal solution. Monte Carlo simulation is conducted for numerical illustration. In order to study the sensitivity of the optimal solution due to mis-specification of parameter values and cost components, a well-designed sensitivity analysis is incorporated using a real-life Type-I hybrid censored data set. [ABSTRACT FROM AUTHOR]

Comparative lifetime experiments are remarkable when the study is to ascertain the relative merits of two competing products regarding the duration of their service life. This paper considers the comparative lifetime experiments of two Gompertz populations under a balanced joint progressive Type-II censoring scheme. The lifetime distributions of the units are assumed to follow the Gompertz distribution with a common shape but different scale parameters. The maximum likelihood estimates of the unknown parameters are derived. The existence of the maximum likelihood estimates is proved. Expectation-maximization and stochastic expectation-maximization algorithms are provided to calculate the estimates. The bootstrap-p, bootstrap-t, and approximate confidence intervals are established. To obtain the Bayesian estimates, it is assumed that the prior of scale parameters is a Beta-Gamma distribution and the prior of the common shape parameter is an independent Gamma distribution. Under squared error loss and LINEX loss functions, the Metropolis-Hastings algorithm is provided to compute the Bayes estimates and the credible intervals. Further, the statistical inferences with order restriction are studied when it is known a priori that the expectation of the lifespan of one population is shorter than that of the other population. A wide range of simulation experiments is conducted to evaluate the performance of the proposed methods. Finally, the lifetimes of white organic light-emitting diodes and the breaking strengths of jute fiber of gauge lengths are analyzed to illustrate the practical application of the proposed model and methods. [ABSTRACT FROM AUTHOR]

The accelerated hazards model is one of the most commonly used models for regression analysis of failure time data and this is especially the case when, for example, the hazard functions may have monotonicity property. Correspondingly a large literature has been established for its estimation or inference when right-censored data are observed. Although several methods have also been developed for its inference based on interval-censored data, they apply only to limited situations or rely on some assumptions such as independent censoring. In this paper, we consider the situation where one observes case K interval-censored data, the type of failure time data that occur most in, for example, medical research such as clinical trials or periodical follow-up studies. For inference, we propose a sieve borrow-strength method and in particular, it allows for informative censoring. The asymptotic properties of the proposed estimators are established. Simulation studies demonstrate that the proposed inference procedure performs well. The method is applied to a set of real data set arising from an AIDS clinical trial. [ABSTRACT FROM AUTHOR]

Numerous variable selection techniques have been developed for complete high-dimensional data but very few of them for censored data. The techniques for complete data must be modified if censoring is present. In this paper, we consider the variable selection technique for accelerated failure time (AFT) models by extending the ranking-based variable selection (RBVS) algorithm and its iterative procedure as proposed in the work of Baranowski et al. through the Stute's weighted least square technique. Simulation studies are conducted to demonstrate the performance of the proposed methods. We further illustrate the performance of this method with a mantle cell lymphoma microarray example. When there is no correlation among the covariates, the proposed method outperforms the iterative sure independence screening and stability selection methods in terms of overall performance for high-dimensional data. Real data analysis also suggests that the proposed method can be chosen for high-dimensional censored data analysis in parallel to other methods in the literature. [ABSTRACT FROM AUTHOR]

Estimation of causal treatment effects has attracted a great deal of interest in many areas including social, biological and health science, and for this, instrumental variable (IV) has become a commonly used tool in the presence of unmeasured confounding. In particular, many IV methods have been developed for right-censored time-to-event outcomes. In this paper, we consider a much more complicated situation where one faces interval-censored time-to-event outcomes, which are ubiquitously present in studies with, for example, intermittent follow-up but are challenging to handle in terms of both theory and computation. A sieve maximum likelihood estimation procedure is proposed for estimating complier causal treatment effects under the additive hazards model, and the resulting estimators are shown to be consistent and asymptotically normal. A simulation study is conducted to evaluate the finite sample performance of the proposed approach and suggests that it works well in practice. It is applied to a breast cancer screening study. [ABSTRACT FROM AUTHOR]

In this paper, we consider a competitive risk scenario in which the initial number of competing risks, assumed to follow a shifted Poisson distribution, is subject to a destructive element. In such settings, both the number of initial risks and risks remaining active after destruction represent missing data. Assuming the population of interest to have a cure component and the form of the data as interval-censored, we extend the destructive shifted Poisson cure model with Weibull lifetimes to accommodate interval-censored data and develop an efficient expectation maximization algorithm for this model. By using the conditional distributions of the missing data, the conditional expected complete log-likelihood function is decomposed into simpler functions which are then maximized independently. An extensive simulation study is carried out to demonstrate the performance of the proposed estimation method through calculated bias, root mean square error, and coverage probability of the asymptotic confidence interval. Also considered is the efficacy of the proposed EM algorithm as compared to direct maximization of the observed log-likelihood function. Finally, data from a crime recidivism study is analyzed for illustrative purpose. [ABSTRACT FROM AUTHOR]

In this paper, we consider a transformation in a random variable which follows a bimodal Birnbaum-Saunders distribution. We propose the unit-bimodal Birnbaum-Saunders (UBBS) distribution and investigate some of its important properties, like cumulative distribution function, moments, survival function and risk function. We apply the UBBS distribution to censored data inflated at zero and one. We used the maximum likelihood approach for parameter estimation and to compare the models. Given the flexibility in UBBS distribution modes, our proposal performs best in beta regression models with zero and/or one excess. [ABSTRACT FROM AUTHOR]

Among the models applied to analyze survival data, a standout is the inverse Gaussian distribution, which belongs to the class of models to analyze positive asymmetric data. However, the variance of this distribution depends on two parameters, which prevents establishing a functional relation with a linear predictor when the assumption of constant variance does not hold. In this context, the aim of this paper is to re-parameterize the inverse Gaussian distribution to enable establishing an association between a linear predictor and the variance. We propose deviance residuals to verify the model assumptions. Some simulations indicate that the distribution of these residuals approaches the standard normal distribution and the mean squared errors of the estimators are small for large samples. Further, we fit the new model to hospitalization times of COVID-19 patients in Piracicaba (Brazil) which indicates that men spend more time hospitalized than women, and this pattern is more pronounced for individuals older than 60 years. The re-parameterized inverse Gaussian model proved to be a good alternative to analyze censored data with non-constant variance. [ABSTRACT FROM AUTHOR]

Linear transformation models have been one type of models commonly used for regression analysis of failure time data partly due to their flexibility. More recently they have been generalised to the case where there may exist a cured subgroup or the censoring may be informative. In this paper, we consider a more complicated and general situation where both a cured subgroup and informative censoring, or more specifically informative interval censoring, exist. As pointed out in the literature, the analysis that fails to take into account either the cured subgroup or the informative censoring can yield biased estimation or misleading conclusions. For the problem, a three-component mixture cure model is presented and we develop a two-step estimation procedure with the use of B-splines to approximate unknown functions. The proposed approach is quite flexible and can be easily implemented. Also the proposed estimators of regression parameters are shown to be consistent and asymptotically normal. An extensive simulation study is conducted and suggests that the method works well for practical situations. Furthermore a real application is provided to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

The generalised maximum likelihood estimator (GMLE) of a survival function S o (t) based on truncated interval-censored (TIC) data has been studied since 1990s (by Frydman, H. (1994), 'A note on nonparametric estimation of the distribution function from interval censored and truncated data', Journal of the Royal Statistical Society, Series B, 56, 71–74 among others). In the literature related to the GMLE based on TIC data, there are several issues that have not been properly settled in both methodology and theory including: (1) innermost intervals based on the TIC data are not correctly formulated and they lead to inconsistent estimators which are not the GMLE; and (2) the consistency of the GMLE has not been established. We settle these two issues in this paper. In particular, we specify the correct forms of innermost intervals and establish consistency results for the GMLE under a realistic model. [ABSTRACT FROM AUTHOR]

In this paper, the inference of multicomponent stress-strength reliability has been derived using progressively censored samples from Topp-Leone distribution. Both stress and strength variables are assumed to follow Topp-Leone distributions with different shape parameters. The maximum likelihood estimate along with the asymptotic confidence interval are developed. Boot-p and Boot-t confidence intervals are also constructed. The Bayes estimates under generalized entropy loss function based on gamma priors using Lindley's, Tierney-Kadane's approximation and Markov chain Monte Carlo methods are derived. A simulation study is considered to check the performance of various estimation methods and different censoring schemes. A real data study shows the applicability of the proposed estimation methods. [ABSTRACT FROM AUTHOR]

In this paper, stress-strength model is studied for an inverted exponential Rayleigh distribution (IERD) when the latent failure times are progressively Type-II censored. When both strength and stress random variables follow common IERD scale parameters, the maximum likelihood estimate of stress-strength reliability (SSR) is established and the associated approximate confidence interval is also constructed using the asymptotic distribution theory and delta method. By constructing pivotal quantities, another alternative generalized estimates for SSR are also proposed for comparison. Moreover, when there are arbitrary strength and stress parameters, likelihood and generalized pivotal based estimates are also presented. In addition, testing problem is gave for comparing the equality of different strength and stress parameters. Finally, simulation study and a real data example are provided for illustration. [ABSTRACT FROM AUTHOR]

In this paper, we study estimation of stress-strength reliability, assuming the stress and strength variables are inverse Gaussian distributed with unknown parameters. When the coefficient of variations of the distributions is unknown but equal, we develop MLE, Bayes estimator, bootstrap interval of the reliability. The profile likelihood Bayes estimator of the coefficient of variation is also derived. When all parameters are different, we derive the MLE, UMVUE, Bayes estimator, bootstrap interval, and highest posterior density credible interval of the stress-strength reliability. The predictive Bayes estimators of the reliability functions are derived. Under progressive type-II censoring, we derive the MLE, Bayes estimator and bootstrap confidence interval. Monte-Carlo simulation results and real data-based examples are also presented. We analyze lung cancer and air pollution data sets as applications of the stress-strength model. [ABSTRACT FROM AUTHOR]

In this paper, we derive the recurrence relations for the single and product moments of progressively Type-II right censored order statistics from the exponential-geometric distribution. For a particular case, these results are reduced to the corresponding results for the usual order statistics. Next, we use these moments to obtain the best linear unbiased estimators of the scale and location-scale parameters of the exponential-geometric distribution based on progressively Type-II right censored samples. The best linear unbiased predictors of future failure times are then discussed. Finally, an illustrative example is presented. [ABSTRACT FROM AUTHOR]

This paper studies the problem about how to design an efficient Bayesian sampling plan based on a simple step-stress test with a random stress-change time for censored data. For brevity, the step-stress test with random stress-change time is briefly called SSRSCT. A Bayesian sampling plan (BSP) through the SSRSCT is called BSPA. First, we derive the BSPA with data based on Type-II censoring for a general loss function. Given gamma and noninformative uniform prior distributions, an explicit expression of the Bayes decision function under a certain loss function is derived. By applying a curtailment procedure to the preceding Bayes decision function, a new Bayesian sampling plan, called an efficient Bayesian sampling plan (EBSPA), is constructed. It is shown that the Bayes risk of EBSPA is less than or equal to that of BSPA. This indicates that EBSPA is more efficient than the BSPA. Comparisons among some BSPAs and the proposed EBSPA are given. Monte Carlo simulations are carried out, and results indicate that the EBSPA outperforms those BSPAs. The EBSPA is recommended. [ABSTRACT FROM AUTHOR]

The aim of the paper is to estimate the unknown parameters of weighted exponential distribution based on the competing risks model under progressively Type-II censoring. It is supposed that the latent causes of failures have weighted exponential distributions with different parameters. The maximum likelihood estimations of four unknown parameters are derived and the uniqueness and existence of them are theoretically proved. Moreover, approximate intervals are proposed and constructed with the delta method and Fisher information matrix. Bootstrap methods are also applied to calculate the confidence intervals. Furthermore, Bayes estimates and the corresponding credible intervals under three various loss functions are computed by using the Monte Carlo Markov Chain method. A simulation study is conducted to assess the statistical performance of all the estimators. Ultimately, real data analysis is provided to illustrate all the statistical inferential procedures developed in the paper. [ABSTRACT FROM AUTHOR]

There is a substantial amount of literature in the area of acceptance sampling plan with censored lifetime data. However, the optimality of a Bayesian sampling plan in the presence of competing risks has not been considered so far. In this paper, first, the Bayesian sampling plans (BSP) for Type-II and Type-I hybrid censoring schemes are discussed in presence of competing risks when the lifetime distribution is exponential. The closed-form expression of the Bayes decision function is obtained analytically for a linear loss function. Then we consider the Weibull distribution with an unknown shape parameter under Type-I hybrid censoring scheme in presence of competing risks to obtain the BSP. However, the Bayes decision function cannot be obtained in closed-form for a general loss function, and in such cases, a numerical algorithm is proposed. As an illustration, in the exponential case, a quadratic loss function, and in Weibull case, a non-polynomial loss function, are considered for the application of the proposed numerical approach to obtain the optimum BSPs using the Bayes decision function. [ABSTRACT FROM AUTHOR]

Semi-parametric transformation models provide a general and flexible class of models for regression analysis of failure time data and many methods have been developed for their estimation. In particular, they include the proportional hazards and proportional odds models as special cases. In this paper, we discuss the situation where one observes left-truncated and interval-censored data, for which it does not seem to exist an established method. For the problem, in contrast to the commonly used conditional approach that may not be efficient, a pairwise pseudo-likelihood method is proposed to recover some missing information in the conditional method. The proposed estimators are proved to be consistent and asymptotically efficient and normal. A simulation study is conducted to assess the empirical performance of the method and suggests that it works well in practical situations. This method is illustrated by using a set of real data arising from an HIV/AIDS cohort study. [ABSTRACT FROM AUTHOR]

In this paper, joint cumulative entropy of progressive type-II censored order statistics is obtained in terms of reversed hazard rate function. Also, entropy and Kullback–Leibler information for progressive type-II censored order statistics are expressed using reversed hazard rate. Optimal life-testing plans based on cumulative entropy are proposed. Finally, cumulative entropy-based optimal designs using compound optimal design strategy for the life-testing experiment under progressive type-II censoring are developed. A real data set is analysed for illustration. [ABSTRACT FROM AUTHOR]

We, in this paper, focus on the inference of conditional quantile difference (CQD) for left-truncated and right-censored model. Based on local conditional likelihood function of the observed data, local likelihood ratio function and smoothed local log-likelihood ratio (log-SLL) of the CQD are constructed, and the maximum local likelihood estimator of the CQD is further defined from the log-SLL. When the observations are assumed to be a sequence of stationary α-mixing random variables, we establish asymptotic normality of the defined estimator, and prove the Wilks' theorem of adjusted log-SLL. Besides, we define another estimator of the CQD based on product-limit estimator of conditional distribution function and give its asymptotic normality. Also, simulation study and real data analysis are conducted to investigate the finite sample behaviour of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, a decision-theoretic approach is used to obtain the Bayesian sampling plan (BSP) for the generalized Type-II hybrid censoring scheme when lifetimes of sampled units follow a one-parameter exponential distribution. An efficient loss function is used to decide whether to accept or reject the batch. The BSP is obtained by constructing the closed form of the Bayes decision function. It is observed that the closed form of the Bayes decision function cannot be obtained analytically for any arbitrary loss function. A numerical approach is proposed to determine the optimum BSP for an arbitrary loss function. To illustrate this, we consider a higher degree polynomial loss function and obtain the optimum BSP numerically. Some numerical studies have been conducted to check the performance of the optimum BSP in different cases. [ABSTRACT FROM AUTHOR]

In this paper, we consider the estimation problem for the semiparametric regression model with censored data in which the number of explanatory variables p in the linear part is much larger than sample size n, often denoted as p n. The purpose of this paper is to study the effects of covariates on a response variable censored on the right by a random censoring variable with an unknown probability distribution. It should be noted that high variance and over-fitting are a major concern in such problems. Ordinary statistical methods for estimation cannot be applied directly to censored and high-dimensional data, and therefore a transformation is required. In the context of this paper, a synthetic data transformation is used for solving the censoring problem. We then apply the LASSO-type double-penalized least squares (DPLS) to achieve sparsity in the parametric component and use smoothing splines to estimate the nonparametric component. A Monte Carlo simulation study is performed to show the performance of the estimators and to analyse the effects of the different censoring levels. A real high-dimensional censored data example is used to illustrate the ideas discussed herein. [ABSTRACT FROM AUTHOR]