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The robustness of the t linear mixed model (tLMM) has been proved and exploited in many applications. Various publications emerged with the aim of proving superiority with respect to traditional linear mixed models, extending to more general settings and proposing more efficient estimation methods. However, little attention has been paid to the mathematical properties of the model itself and to the evaluation of the proposed estimation methods. In this paper we perform an in-depth analysis of the tLMM, evaluating a direct maximum likelihood estimation method via an intensive simulation study and investigating some identifiability properties. The theoretical findings are illustrated through an application to a dataset collected from a sleep trial. [ABSTRACT FROM AUTHOR]

Ordinary differential equations (ODEs) are important mathematical models in applied sciences to describe dynamic processes. The parameters involved in the models usually have specific meanings, and hence need to be estimated from the observed data. In applications, the parameters may change with time, which are called time-varying parameters. In this paper, we propose a Bayesian penalized B-spline method to estimate the time-varying parameters and initial values in ODEs. Simulation studies show that this method is more efficient than the two-stage local polynomial method. Furthermore, we introduce the DIC model selection criterion to determine the number of knots of B-splines. [ABSTRACT FROM AUTHOR]

In the field of computer virus, a growing number of mathematical models have been published during the last decade. In this paper, we consider several estimation methods under two parametric models, the random constant scanning model and the nonhomogeneous random scanning model, to propose a comparison of the estimators’ performances based on the simulation of random populations. We conclude our work with an application of the different estimation methods to a real data set of worm propagation. [ABSTRACT FROM AUTHOR]

Acceptance sampling is a quality assurance tool, which provides a rule for the producer and the consumer to make acceptance or rejection decision about a lot. This paper attempts to develop a more efficient sampling plan, variables repetitive group sampling plan, based on the total loss to the producer and consumer. To design this model, two constraints are considered to satisfy the opposing priorities and requirements of the producer and the consumer by using Acceptable quality level (AQL) and Limiting quality level (LQL) points on operating characteristic (OC) curve. The objective function of this model is constructed based on the total expected loss. In order to illustrate the application of the proposed model, an example is presented. In addition, the effects of process parameters on the optimal solution and the total expected loss are studied by performing a sensitivity analysis. Finally, the efficiency of the proposed model is compared with the variables single sampling plan, the variables double sampling plan and the repetitive group sampling plan of Balamurali and Jun (2006) in terms of average sample number, total expected loss and its difference with ideal OC curve. [ABSTRACT FROM AUTHOR]

In Balanced Sampling Plans Excluding Adjacent Units (BSA plans) first order inclusion probabilities are equal and second order inclusion probabilities are zero for pairs of units at a distance less than or equal to m and are constant for pairs of units which are at a distance greater than m. These plans are useful when the adjacent units in the population provide similar information. In this paper, an algorithm based on linear programming approach has been developed for construction of two-dimensional BSA plans under sharing a border and island adjacency schemes for m ≤ 2. Some results on existence of such BSA plans have also been obtained for each adjacency scheme separately. [ABSTRACT FROM AUTHOR]

Preventive maintenance (PM) scheduling of units is addressed as a crucial issue that effects on both economy and reliability of power systems. In this paper, we describe an application of statistical analysis for determining the best PM strategy in the case of parallel, series, and single-item replacement systems. A key aspect of industrial maintenance is the trade-off between cost and time of performing PM operations. The goals of this study is to determine the best time for performing PM operations in each system and also finding the number of spare parts and facilities in single-item replacement and parallel systems respectively so that the average cost per unit time is minimized. In this proposed maintenance strategy, PM operations are regularly performed on the production unit in equal time intervals. Finally, three examples are presented to demonstrate the effectiveness of the proposed models. [ABSTRACT FROM AUTHOR]

In the multistage processes, quality of a process or a product at each stage is related to the previous stage(s). This property is referred to as a cascade property. Sometimes, quality of a process is characterized by a profile. In this paper, we consider a two-stage process with a normal quality characteristic in the first stage and a simple linear regression profile in the second stage. Then we propose two methods to monitor quality characteristics in both stages. The performance of the proposed two methods is evaluated through a numerical example in terms of average run length criterion. [ABSTRACT FROM PUBLISHER]

In this paper, we conduct a Monte Carlo simulation study to evaluate three propensity score (PS) scenarios for estimating an average treatment effect (ATE) in observational studies when treatment switching exists: (a) ignoring treatment switching in subjects (UPS), (b) removing subjects with treatment switching (RPS), and (c) adjusting for treatment switching effect (APS) with two inverse probability weighting estimators, IPW1 and IPW2. We evaluate these six estimators in terms of bias, mean squared error (MSE), empirical standard error (ESE), and coverage probability (CP) under various simulation scenarios. Simulation results show that the IPW2 estimator with RPS has relatively good performance. [ABSTRACT FROM AUTHOR]

Neighbor designs are useful to neutralize the neighbor effects. In this paper two classes of these designs are constructed in circular binary blocks of size 4, 8, …, 24. First class consists of six infinite series of nearest neighbor designs in which each pair of distinct treatments appears once as neighbors. Second class also deals with six infinite series of these designs in which each pair of distinct treatments appears twice as neighbors. A catalog of nearest neighbor designs is also compiled in circular binary blocks for odd number of treatments from 23 to 99. [ABSTRACT FROM AUTHOR]

This paper is the generalization of weight-fused elastic net (Fu and Xu, 2012), which performs group variable selection by combining weight-fused LASSO(wfLasso) and elastic net (Zou and Hastie, 2005) penalties. In this study, the elastic net penalty is replaced by adaptive elastic net penalty (AdaEnet) (Zou and Zhang, 2009), and a new group variable selection algorithm with oracle property (Fan and Li, 2001; Zou, 2006) is obtained. [ABSTRACT FROM PUBLISHER]

In this article, we consider the mean remaining strength of ak-out-of-n:Fsystem in the stress–strength setup for the exchangeable components. We provide some results for parallel and series systems under this setup, whereX1,X2, …,Xnare the strengths of the components designed under the common stress. An illustrative example is given for thek-out-of-n:Fsystem using the multivariate FGM distribution. [ABSTRACT FROM PUBLISHER]

This research examines the statistical methodology that is used to estimate the parameters in item response models. An integral part of an item response model is the normalization rule that is used to identify the distributional parameters. The main result shown here is that only Verhelst-Glas normalizations that arbitrarily set one difficulty and one dispersion parameter to unity are consistent with the basic assumptions underlying the two-parameter logistic model. Failure to employ this type of normalization will lead to scores that depend on the item composition of the test and differential item difficulty (DIF)will compromise the validity of the estimated ability scores when different groups are being compared. It is also shown that some of the tests for DIF fail when the data are generated by an IRT model with a random effect.Most of the results are based on simulations of a four item model. Because the data generation mechanism is known, it is possible to determine the effect on ability scores and parameter estimates when different normalizations or different distribution parameter values are used. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In queuing theory, a major interest of researchers is studying the behavior and formation process and analyzing the performance characteristics of queues, particularly the traffic intensity, which is defined as the ratio between the arrival rate and the service rate. How these parameters can be estimated using some statistical inferential method is the mathematical problem treated here. This article aims to obtain better Bayesian estimates for the traffic intensity of M/M/1 queues, which, in Kendall notation, stand for Markovian single-server infinity queues. The Jeffreys prior is proposed to obtain the posterior and predictive distributions of some parameters of interest. Samples are obtained through simulation and some performance characteristics are analyzed. It is observed from the Bayes factor that Jeffreys prior is competitive, among informative and non-informative prior distributions, and presents the best performance in many of the cases tested. [ABSTRACT FROM AUTHOR]

In this article, we studied the identification of significant predictors in partially linear model in which some regressors are contaminated with random errors. Moreover, the dimension of parametric component is divergent and the regression coefficients are sparse. We applied difference technique to remove the nonparametric component for circumventing the selection of bandwidth, and constructed a bias-corrected shrinking estimator for the coefficient by using smoothly clipped absolute deviation (SCAD) penalty. Then, we derived the estimating and selecting consistency and established the asymptotic distribution for the identified significant estimators. Finally, Monte Carlo studies illustrate the performance of our approach. [ABSTRACT FROM AUTHOR]

In this article, we propose the two control charts, i.e. the 'VMAX Group Runs' (VMAX-GR) and 'VMAX Modified Group Runs' (VMAX-MGR) control charts based on the bivariate normal processes, for monitoring the covariance matrix. The proposed charts give the faster detection of a process change and have better diagnostic feature. It is verified that the VMAX-GR and the VMAX-MGR charts give a significant reduction in the out-of-control 'Average Run Length' (ARL) in the zero state, as well as in the steady state, as compared to the synthetic control chart based on the VMAX statistic and the generalized variance ∣S∣ chart. [ABSTRACT FROM AUTHOR]

Overdispersion is a problem encountered in the analysis of count data that can lead to invalid inference if unaddressed. Decision about whether data are overdispersed is often reached by checking whether the ratio of the Pearson chi-square statistic to its degrees of freedom is greater than one; however, there is currently no fixed threshold for declaring the need for statistical intervention. We consider simulated cross-sectional and longitudinal datasets containing varying magnitudes of overdispersion caused by outliers or zero inflation, as well as real datasets, to determine an appropriate threshold value of this statistic which indicates when overdispersion should be addressed. [ABSTRACT FROM AUTHOR]

In this article, we consider the destructive length-biased Poisson cure rate model, proposed by Rodrigues et al., that presents a realistic and interesting interpretation of the biological mechanism for the recurrence of tumor in a competing causes scenario. Assuming the lifetime to follow the Weibull distribution and censoring mechanism to be non-informative, the necessary steps of the EM algorithm for the determination of the MLEs of the model parameters are developed here based on right censored data. The standard errors of the MLEs are obtained by inverting the observed information matrix. A simulation study is then carried out to examine the method of inference developed here. Finally, the proposed methodology is illustrated with a real melanoma dataset. [ABSTRACT FROM AUTHOR]

The quality characteristic is usually measured by ordered attribute levels, such as good, general, and poor, which describe different magnitudes of the characteristic. The ordinal levels are determined by a continuous latent variable, the shifts of which are reflected by the observed counts in each level. This article devises a control procedure based on the discrepancy between observed average cumulative counts and their expected ones. Simulation results are shown to demonstrate its superior sensitivity in simultaneously detecting location and dispersion shifts of the latent variable. Flexibility in assigning the weight for each level can allow the chart to be more powerful. [ABSTRACT FROM AUTHOR]

In many life-testing and reliability experiments, data are often censored in order to reduce the cost and time associated with testing and since the conventional Type-I and Type-II censoring schemes are not flexible enough, progressive censoring is developed by researchers. In this article, we develop a general goodness of fit test by using a new estimate of Kullback–Leibler information based on progressively Type-II censored data. Consistency and other properties of the proposed test are shown. Then, we use the proposed test statistic to test for exponentiality based on progressively Type-II censored data. The power values of the proposed test under different progressively Type-II censoring schemes are computed, through Monte Carlo simulations. It is observed that the proposed test is quite powerful in compared with the test proposed by Balakrishnan et al. (2007). Two real datasets from progressive censoring literature are finally presented for illustrative purpose. [ABSTRACT FROM AUTHOR]

This work aimed at proposing a procedure based on the cumulative distribution of maximums and minimums to identify outliers in generalized Gamma-response models. In order to validate such method, we used simulations scenarios defined by the combination of different samples, contamination rate and distributions with different degrees of asymmetry. In this context, probabilities related to errors in classification and accuracy were obtained by carrying by Monte Carlo simulations. Using cumulative distribution of extremes to identify outliers in a Gamma-response model is recommended, since it is not likely to present errors and was highly accurate in all assessed scenarios. [ABSTRACT FROM AUTHOR]

The inverted generalized exponential distribution is defined as an alternative model for lifetime data. The existence of moments of this distribution is shown to hold under some restrictions. However, all the moments exist for the truncated inverted generalized exponential distribution and closed-form expressions for them are derived in this article. The distributional properties of this truncated distribution are studied. Maximum likelihood estimation method is discussed for the estimation of the parameters of the distribution both theoretically and empirically. In order to see the modeling performance of the distribution, two real datasets are analyzed. [ABSTRACT FROM AUTHOR]

In this article, we study the volatility in the monthly price series of edible oils in domestic and international markets using the two popular family of nonlinear time-series models, viz, Generalized autoregressive conditional heteroscedastic (GARCH) models and Stochastic volatility (SV) models. To improve the forecasts of the volatility process, we also propose a new method of combining the volatility of these two competing models using the powerful technique of Kalman filter. The individual models as well as the combined models are assessed on their ability to predict the correct directional change (CDC) in future values as well as other goodness-of-fit statistics. Further, forecasting performance are also evaluated by computing various measures to validate the proposed methodology. [ABSTRACT FROM AUTHOR]

Variable selection is an effective methodology for dealing with models with numerous covariates. We consider the methods of variable selection for semiparametric Cox proportional hazards model under the progressive Type-II censoring scheme. The Cox proportional hazards model is used to model the influence coefficients of the environmental covariates. By applying Breslow’s “least information” idea, we obtain a profile likelihood function to estimate the coefficients. Lasso-type penalized profile likelihood estimation as well as stepwise variable selection method are explored as means to find the important covariates. Numerical simulations are conducted and Veteran’s Administration Lung Cancer data are exploited to evaluate the performance of the proposed method. [ABSTRACT FROM PUBLISHER]

The finite distributed lag models include highly correlated variables as well as lagged and unlagged values of the same variables. Some problems are faced for this model when applying the ordinary least squares (OLS) method or econometric models such as Almon and Koyck models. The primary aim of this study is to compare performances of alternative estimators to the OLS estimator defined by combining the Almon estimator with some estimators using Almon (1965) data. A simulation study with different model parameters is performed and the estimators are compared according to the root mean square error (RMSE) and prediction mean square error (PMSE). [ABSTRACT FROM AUTHOR]

The authors focus discussion on estimation of the proportion ratio (PR) in the presence of residual effects under the AB/BA design. Under a randomeffects multiplicative risk model,we develop three point estimators and three interval estimators accounting for residual effects for the PR. Using Monte Carlo simulations, we compare the performance of these point (or interval) estimators with point (or interval) estimators assuming no residual effects with respect to the bias and mean-squared-error (or the coverage probability and average length). The authors use the data taken from an AB/BA trial comparing two new inhalation devices to illustrate the use of these estimators. [ABSTRACT FROM AUTHOR]

A flexible Bayesian semiparametric accelerated failure time (AFT) model is proposed for analyzing arbitrarily censored survival data with covariates subject to measurement error. Specifically, the baseline error distribution in the AFT model is nonparametrically modeled as a Dirichlet process mixture of normals. Classical measurement error models are imposed for covariates subject to measurement error. An efficient and easy-to-implement Gibbs sampler, based on the stick-breaking formulation of the Dirichlet process combined with the techniques of retrospective and slice sampling, is developed for the posterior calculation. An extensive simulation study is conducted to illustrate the advantages of our approach. [ABSTRACT FROM AUTHOR]

The close relationship between quality and maintenance of manufacturing systems has contributed to the development of integrated models which use the concept of statistical process control (SPC) and maintenance. This article demonstrates the integration of the Shewhart individual-residual (ZX− Ze ) joint control chart and maintenance for two-stage dependent processes by jointly optimizing their policies to minimize the expected total costs associated with quality, maintenance and inspection. To evaluate the effectiveness of the proposed model, two stand-alone models—a maintenance model and an SPC model—are proposed. Then a numerical example is given to illustrate the application of the proposed integrated model. The results show that the integrated model outperforms the two stand-alone models with regard to the expected cost per unit time. Finally, a sensitivity analysis is conducted to develop insights into time parameters and cost parameters that influence the integration efforts. [ABSTRACT FROM AUTHOR]

Nonlinear mixed effects models (NLMEM) are used in pharmacokinetics to analyse concentrations of patients during drug development, particularly for pediatric studies. Approaches based on the Fisher information matrix can be used to optimize their design. Local design needs some a priori parameter values which might be difficult to guess. Therefore, two-stage adaptive designs are useful to provide some flexibility. We implemented in the R function PFIM the Fisher matrix for two-stage designs in NLMEM. We evaluated, with simulations, the impact of one-stage and two-stage designs on the precision of parameter estimation when the true and a priori parameters are different. [ABSTRACT FROM PUBLISHER]

Seemingly unrelated regression (SUR) method is applied to the instrumental variable (IV) estimation of the canonical contagion models. A finite sample Monte Carlo experiment shows that the resulting estimator, IV-SUR estimator, is substantially better than the existing IV estimator in terms of both bias and mean squares error under diverse circumstance of instrument, conditional heteroscedasticity, and cross-section correlation. [ABSTRACT FROM PUBLISHER]

This article summarizes and discusses the existing p-value pooling approaches and compares their performances in the context of panel unit root tests. When the data are free of contemporaneous correlation, most tests achieve very high power. However, in the presence of contemporaneous correlation, most tests suffer from moderate to severe size distortions. When the panel contains both stationary and nonstationary series, the power of tests increases as the cross-sectional units grows. Among all the tests under study, the mean-of-Z test yields the highest power for the benchmark model, while the Fisher test is most robust for complicated model structures. [ABSTRACT FROM AUTHOR]

In this study, we define the Pólya–Aeppli process of order k as a compound Poisson process with truncated geometric compounding distribution with success probability 1 − ρ > 0 and investigate some of its basic properties. Using simulation, we provide a comparison between the sample paths of the Pólya–Aeppli process of order k and the Poisson process. Also, we consider a risk model in which the claim counting process {N(t)} is a Pólya-Aeppli process of order k, and call it a Pólya—Aeppli of order k risk model. For the Pólya–Aeppli of order k risk model, we derive the ruin probability and the distribution of the deficit at the time of ruin. We discuss in detail the particular case of exponentially distributed claims and provide simulation results for more general cases. [ABSTRACT FROM AUTHOR]

The logistic regression model is used when the response variables are dichotomous. In the presence of multicollinearity, the variance of the maximum likelihood estimator (MLE) becomes inflated. The Liu estimator for the linear regression model is proposed by Liu to remedy this problem. Urgan and Tez and Mansson et al. examined the Liu estimator (LE) for the logistic regression model. We introduced the restricted Liu estimator (RLE) for the logistic regression model. Moreover, a Monte Carlo simulation study is conducted for comparing the performances of the MLE, restricted maximum likelihood estimator (RMLE), LE, and RLE for the logistic regression model. [ABSTRACT FROM AUTHOR]

This article is aimed at reviewing a novel Bayesian approach to handle inference and estimation in the class of generalized nonlinear models. These models include some of the main techniques of statistical methodology, namely generalized linear models and parametric nonlinear regression. In addition, this proposal extends to methods for the systematic treatment of variation that is not explicitly predicted within the model, through the inclusion of random effects, and takes into account the modeling of dispersion parameters in the class of two-parameter exponential family. The methodology is based on the implementation of a two-stage algorithm that induces a hybrid approach based on numerical methods for approximating the likelihood to a normal density using a Taylor linearization around the values of current parameters in an MCMC routine. [ABSTRACT FROM AUTHOR]

We consider the fixed and exponential time-stepping Euler algorithms, with boundary tests, to calculate the mean first exit times (MFET) of two one-dimensional neural diffusion models, represented by the Ornstein–Uhlenbeck (OU) process and a stochastic space-clamped FitzHugh–Nagumo (FHN) system. The numerical methods are described and the convergence rates for the MFET analyzed. A boundary test improves the rate of convergence from order one-half to order 1. We show how to apply the multi-level Monte Carlo (MLMC) method to an Euler time-stepping method with boundary test and this improves the Monte Carlo computation of the MFET. [ABSTRACT FROM PUBLISHER]