Statistical inference of Type-I progressively censored step-stress accelerated life test with dependent competing risksBai, Xuchao; Shi, Yimin; Ng, Hon Keung Tony
doi: 10.1080/03610926.2020.1788081pmid: N/A
Abstract This paper considers a step-stress accelerated dependent competing risks model under progressively Type-I censoring schemes. The dependence structure between competing risks is modeled by a general bivariate function, the cumulative exposure model is assumed and the accelerated model is described by the power rule model. The point and interval estimation of the model parameters and the reliability under normal usage level at mission time are obtained by using the maximum likelihood method and the asymptotic normal theory. We also consider the Bayesian estimators and the highest posterior density credible intervals based on conjugate priors, E-Bayesian, hierarchical Bayesian and empirical Bayesian methods. To illustrate the proposed methodology, the Marshall-Olkin bivariate exponential distribution is used to model the dependence structure between competing risks. A Monte Carlo simulation study and a real data analysis are presented to study the performance of different estimation methods.
New results on stochastic comparisons of finite mixtures for some families of distributionsNadeb, Hossein; Torabi, Hamzeh
doi: 10.1080/03610926.2020.1788082pmid: N/A
Abstract The classical finite mixture model is an effective tool to describe the lifetimes of the items existing in a random sample which are selected from some heterogeneous populations. This paper carries out stochastic comparisons between two classical finite mixture models in the sense of the usual stochastic order, when the subpopulations follow a wide class of distributions including the scale model, the proportional hazard rate model and the proportional reversed hazard rate model. Next, we consider the hazard rate and dispersive orders when the subpopulations follow the proportional hazard rate model and also the reversed hazard rate order in the case that the subpopulations follow the proportional reversed hazard rate model. Finally, the likelihood ratio order between two finite mixtures is characterized when the subpopulations belong to the transmuted-G model.
Robust tests of the equality of two high-dimensional covariance matricesZi, Xuemin; Chen, Hui
doi: 10.1080/03610926.2020.1788085pmid: N/A
Abstract It is of great importance in both theory and application to test the equality of two covariance matrices and . This article proposes a new robust test based on spatial sign statistic regarding in high-dimensional setting, and shows that the test statistic is asymptotically normal under elliptical distribution. Besides theoretical properties, simulation results also show that the new test significantly outperforms existing methods in terms of size and power for non normal and high-dimensional data. Analysis of colon cancer data set is carried out to demonstrate the application of the testing procedure.
Confidence distributions and empirical Bayes posterior distributions unified as distributions of evidential supportBickel, David R.
doi: 10.1080/03610926.2020.1790004pmid: N/A
Abstract While empirical Bayes methods thrive in the presence of the thousands of simultaneous hypothesis tests in genomics and other large-scale applications, significance tests and confidence intervals are considered more appropriate for small numbers of tested hypotheses. Indeed, for fewer hypotheses, there is more uncertainty in empirical Bayes estimates of the prior distribution. Confidence intervals have been used to propagate the uncertainty in the prior to empirical Bayes inference about a parameter, but only by combining a Bayesian posterior distribution with a confidence distribution. Combining distributions of both types has also been used to combine empirical Bayes methods and confidence intervals for estimating a parameter of interest. To clarify the foundational status of such combinations, the concept of an evidential model is proposed. In the framework of evidential models, both Bayesian posterior distributions and confidence distributions are special cases of evidential support distributions. Evidential support distributions, by quantifying the sufficiency of the data as evidence, leverage the strengths of Bayesian posterior distributions and confidence distributions for cases in which each type performs well and for cases benefiting from the combination of both. Evidential support distributions also address problems of bioequivalence, bounded parameters, and the lack of a unique confidence distribution.
Higher order calibrated estimator in two-stage samplingSalinas, Veronica I.; Sedory, Stephen A.; Singh, Sarjinder
doi: 10.1080/03610926.2020.1790005pmid: N/A
Abstract In this paper, we consider a situation when the population variances of the auxiliary variable in the first stage units selected in a sample are known in addition to the known population means of the auxiliary variable. The higher order calibration weights which make use of both the population variances and population means at the estimation stage for both the first stage units and the second stage units selected in the sample are derived. The resultant estimator is found to be consistent estimator, and has variance smaller than the existing estimators in the literature. The percent relative efficiency of the proposed estimator over the linear regression estimator has been demonstrated through numerical comparisons.
The queue revisitedGoswami, Veena; Chaudhry, M. L.
doi: 10.1080/03610926.2020.1790602pmid: N/A
Abstract We present analytic expressions (in terms of roots of the underlying characteristic equation) for the steady-state distributions of the number of customers for the finite-state queueing model with partial-batch rejection policy. We obtain the system-length distributions at a service-completion epoch by applying the imbedded Markov chain technique. Using the roots of the related characteristic equation, the method leads to giving a unified approach for solving both finite- and infinite-buffer systems. We find relationships between system-length distributions at departure, random, and arrival epochs using discrete renewal theory and conditioning on the system states. Based on these relationships, we obtain various performance measures and provide numerical results for the same. We also perform computational analysis and compare our results with respect to the solution obtained by solving a linear system of equations in terms of running times.
New shrinkage parameters for the inverse Gaussian Liu regressionNaveed, Khalid; Amin, Muhammad; Afzal, Saima; Qasim, Muhammad
doi: 10.1080/03610926.2020.1791339pmid: N/A
Abstract In the Inverse Gaussian Regression (IGR), there is a significant increase in the variance of the commonly used Maximum Likelihood (ML) estimator in the presence of multicollinearity. Alternatively, we suggested the Liu Estimator (LE) for the IGR that is the generalization of Liu. In addition, some estimation methods are proposed to estimate the optimal value of the Liu shrinkage parameter, d. We investigate the performance of these methods by means of Monte Carlo Simulation and a real-life application where Mean Squared Error (MSE) and Mean Absolute Error (MAE) are considered as performance criteria. Simulation and application results show the superiority of new shrinkage parameters to the ML estimator under certain condition.
Nonparametric smoothed quantile difference estimation for length-biased and right-censored dataShi, Jianhua; Liu, Yutao; Xu, Jinfeng
doi: 10.1080/03610926.2020.1791340pmid: N/A
Abstract We consider the nonparametric analysis of length-biased and right-censored data (LBRC) by quantile difference. With its desirable properties such as superior robustness and easy interpretation, quantile difference has been widely used in practice, in particular, for missing and survival data. Existing approaches for nonparametric estimation of quantile difference in length-biased survival data, however, exhibit some drawbacks such as non-smoothness and instabilities. To overcome these difficulties, we proposed a smoothed quantile difference estimation approach to improve its estimating efficiency with its validity justified by asymptotic theories. Simulations are also conducted to evaluate the performance of the proposed estimator. An application to the Channing house data is further provided for illustration.