On generalized exponential chain ratio estimators under stratified two-phase random sampling

Sanaullah et al. (2014 Sanaullah, A., Ali, H.M., Noor ul Amin, M., Hanif, M. (2014). Generalized exponential chain ratio estimators under stratified two-phase random sampling. Appl. Math. Comput. 226:541–547.[Crossref], [Web of Science ®] , [Google Scholar]) have suggested generalized exponential chain ratio estimators under stratified two-phase sampling scheme for estimating the finite population mean. However, the bias and mean square error (MSE) expressions presented in that work need some corrections, and consequently the study based on efficiency comparison also requires corrections. In this article, we revisit Sanaullah et al. (2014 Sanaullah, A., Ali, H.M., Noor ul Amin, M., Hanif, M. (2014). Generalized exponential chain ratio estimators under stratified two-phase random sampling. Appl. Math. Comput. 226:541–547.[Crossref], [Web of Science ®] , [Google Scholar]) estimator and provide the correct bias and MSE expressions of their estimator. We also propose an estimator which is more efficient than several competing estimators including the classes of estimators in Sanaullah et al. (2014 Sanaullah, A., Ali, H.M., Noor ul Amin, M., Hanif, M. (2014). Generalized exponential chain ratio estimators under stratified two-phase random sampling. Appl. Math. Comput. 226:541–547.[Crossref], [Web of Science ®] , [Google Scholar]). Three real datasets are used for efficiency comparisons.     

A Bayesian Approach for Nonlinear Regression Models with Continuous Errors

Abstract

In this paper we develop a Bayesian analysis for the nonlinear regression model with errors that follow a continuous autoregressive process. In this way, unequally spaced observations do not present a problem in the analysis. We employ the Gibbs sampler, (see Gelfand, A., Smith, A. (1990 Gelfand, A. and Smith, A. 1990. Sampling based approaches to calculating marginal densities. J. Amer. Statist. Assoc., 85: 398–409. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). Sampling based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85:398–409.), as the foundation for making Bayesian inferences. We illustrate these Bayesian inferences with an analysis of a real data-set. Using these same data, we contrast the Bayesian approach with a generalized least squares technique.     

A Computational Bayesian Method for Generalized Semiparametric Regression Models

To better understand the power shift and the U.S. role compared to China and others regional actors, the Chicago Council on Global Affairs and the East Asia Institute (EAI) surveyed people in six countries - China, Japan, South Korea, Vietnam, Indonesian, and the United States - in the first half of 2008 about regional security and economic integration in Asia and about how these nations perceive each other (Bouton et al., 2010 Bouton, M., Steven, K., Benjamin, P., and Gregory, H. (2010). Soft power in Asia survey, 2008. ICPSR25342-v1. Ann Arbor, MI: Inter-university Consortium for Political and Social Research [distributor], 2010-04-05. doi:10.3886/ICPSR25342.v1[Crossref] , [Google Scholar]). There exists latent variance that cannot be adequately explained by parametric models. This is, in large part, due to the hidden structures and latent stories that from in unexpected ways. Therefore, a new Gibbs sampler is developed here in order to reveal preciously unseen structures and latent variances found in the survey dataset of Bouton et al. This new sampler is based upon the semiparametric regression, a well-known tool frequently utilized in order to capture the functional dependence between variables with fixed effect parametric and nonlinear regression. This is then extended to a generalized semiparametric regression for binary responses with logit and probit link function. The new sampler is then developed for the generalized linear mixed model with a nonparametric random effect. It is expressed as nonparametric regression with the multinomial-Dirichlet distribution for the number and positions of knots.     

Weighting variables in Kohonen competitive learning algorithms

This paper presents a new variable weight method, called the singular value decomposition (SVD) approach, for Kohonen competitive learning (KCL) algorithms based on the concept of Varshavsky et al. [18 R. Varshavsky, A. Gottlieb, M. Linial, and D. Horn, Novel unsupervised feature filtering of bilogical data, Bioinformatics 22 (2006), pp. 507–513.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]. Integrating the weighted fuzzy c-means (FCM) algorithm with KCL, in this paper, we propose a weighted fuzzy KCL (WFKCL) algorithm. The goal of the proposed WFKCL algorithm is to reduce the clustering error rate when data contain some noise variables. Compared with the k-means, FCM and KCL with existing variable-weight methods, the proposed WFKCL algorithm with the proposed SVD's weight method provides a better clustering performance based on the error rate criterion. Furthermore, the complexity of the proposed SVD's approach is less than Pal et al. [17 S.K. Pal, R.K. De, and J. Basak, Unsupervised feature evaluation: a neuro-fuzzy approach, IEEE. Trans. Neural Netw. 11 (2000), pp. 366–376.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]], Wang et al. [19 X.Z. Wang, Y.D. Wang, and L.J. Wang, Improving fuzzy c-means clustering based on feature-weight learning, Pattern Recognit. Lett. 25 (2004), pp. 1123–1132.[Crossref], [Web of Science ®] , [Google Scholar]] and Hung et al. [9 W. -L. Hung, M. -S. Yang, and D. -H. Chen, Bootstrapping approach to feature-weight selection in fuzzy c-means algorithms with an application in color image segmentation, Pattern Recognit. Lett. 29 (2008), pp. 1317–1325.[Crossref], [Web of Science ®] , [Google Scholar]].     

Multiple dependent state repetitive sampling plans based on one-sided process capability indices

In this research, multiple dependent state and repetitive group sampling are used to design a variable sampling plan based on one-sided process capability indices, which consider the quality of the current lot as well as the quality of the preceding lots. The sample size and critical values of the proposed plan are determined by minimizing the average sample number while satisfying the producer's risk and consumer's risk at corresponding quality levels. In addition, comparisons are made with the existing sampling plans [Pearn and Wu (2006a Pearn, W. L., and C. W. Wu. 2006a. Critical acceptance values and sample sizes of a variables sampling plan for very low fraction of defectives. Omega: International Journal of Management Science 34 (1):90–101.[Crossref], [Web of Science ®] , [Google Scholar]), Yen et al. (2015 Yen, C. H., C. H. Chang, and M. Aslam. 2015. Repetitive variable acceptance sampling plan for one-sided specification. Journal of Statistical Computation and Simulation 85 (6):1102–16.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar])] in terms of average sample number and operating characteristic curve. Finally, an example is provided to illustrate the proposed plan.     

A new efficient unrelated randomized response model

The present paper suggests an interesting and useful ramification of the unrelated randomized response model due to Pal and Singh (2012 Pal, S., and S. Singh. 2012. A new unrelated question randomized response model. Statistics 46 (1):99–109.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) [A new unrelated question randomized response model. Statistics 46 (1), 99–109] that can be used for any sampling scheme. We have shown theoretically and numerically that the proposed model is more efficient than Pal and Singh (2012 Pal, S., and S. Singh. 2012. A new unrelated question randomized response model. Statistics 46 (1):99–109.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) model.     

An efficient use of moment's ratios of scrambling variables in a randomized response technique

This paper aimed at providing an efficient new unbiased estimator for estimating the proportion of a potentially sensitive attribute in survey sampling. The suggested randomization device makes use of the means, variances of scrambling variables, and the two scalars lie between “zero” and “one.” Thus, the same amount of information has been used at the estimation stage. The variance formula of the suggested estimator has been obtained. We have compared the proposed unbiased estimator with that of Kuk (1990 Kuk, A.Y.C. (1990). Asking sensitive questions inderectely. Biometrika 77:436–438.[Crossref], [Web of Science ®] , [Google Scholar]) and Franklin (1989 Franklin, L.A. (1989). A comparision of estimators for randomized response sampling with continuous distribution s from a dichotomous population. Commun. Stat. Theor. Methods 18:489–505.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), and Singh and Chen (2009 Singh, S., Chen, C.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. J. Stat. Plann. Inference. 139:3377–3380.[Crossref], [Web of Science ®] , [Google Scholar]) estimators. Relevant conditions are obtained in which the proposed estimator is more efficient than Kuk (1990 Kuk, A.Y.C. (1990). Asking sensitive questions inderectely. Biometrika 77:436–438.[Crossref], [Web of Science ®] , [Google Scholar]) and Franklin (1989 Franklin, L.A. (1989). A comparision of estimators for randomized response sampling with continuous distribution s from a dichotomous population. Commun. Stat. Theor. Methods 18:489–505.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and Singh and Chen (2009 Singh, S., Chen, C.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. J. Stat. Plann. Inference. 139:3377–3380.[Crossref], [Web of Science ®] , [Google Scholar]) estimators. The optimum estimator (OE) in the proposed class of estimators has been identified which finally depends on moments ratios of the scrambling variables. The variance of the optimum estimator has been obtained and compared with that of the Kuk (1990 Kuk, A.Y.C. (1990). Asking sensitive questions inderectely. Biometrika 77:436–438.[Crossref], [Web of Science ®] , [Google Scholar]) and Franklin (1989 Franklin, L.A. (1989). A comparision of estimators for randomized response sampling with continuous distribution s from a dichotomous population. Commun. Stat. Theor. Methods 18:489–505.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) estimator and Singh and Chen (2009 Singh, S., Chen, C.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. J. Stat. Plann. Inference. 139:3377–3380.[Crossref], [Web of Science ®] , [Google Scholar]) estimator. It is interesting to mention that the “optimum estimator” of the class of estimators due to Singh and Chen (2009 Singh, S., Chen, C.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. J. Stat. Plann. Inference. 139:3377–3380.[Crossref], [Web of Science ®] , [Google Scholar]) depends on the parameter π under investigation which limits the use of Singh and Chen (2009 Singh, S., Chen, C.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. J. Stat. Plann. Inference. 139:3377–3380.[Crossref], [Web of Science ®] , [Google Scholar]) OE in practice while the proposed OE in this paper is free from such a constraint. The proposed OE depends only on the moments ratios of scrambling variables. This is an advantage over the Singh and Chen (2009 Singh, S., Chen, C.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. J. Stat. Plann. Inference. 139:3377–3380.[Crossref], [Web of Science ®] , [Google Scholar]) estimator. Numerical illustrations are given in the support of the present study when the scrambling variables follow normal distribution. Theoretical and empirical results are very sound and quite illuminating in the favor of the present study.     

Longitudinal profiles of bounded outcome scores as predictors for disease activity in rheumatoid arthritis patients: a joint modeling approach

A variety of statistical approaches have been suggested in the literature for the analysis of bounded outcome scores (BOS). In this paper, we suggest a statistical approach when BOSs are repeatedly measured over time and used as predictors in a regression model. Instead of directly using the BOS as a predictor, we propose to extend the approaches suggested in [16 E. Lesaffre, D. Rizopoulos, and R. Tsonaka, The logistics-transform for bounded outcome scores, Biostatistics 8 (2007), pp. 72–85. doi: 10.1093/biostatistics/kxj034[Crossref], [PubMed], [Web of Science ®] , [Google Scholar],21 M. Molas and E. Lesaffre, A comparison of the three random effects approaches to analyse repeated bounded outcome scores with an application in a stroke revalidation study, Stat. Med. 27 (2008), pp. 6612–6633. doi: 10.1002/sim.3432[Crossref], [PubMed], [Web of Science ®] , [Google Scholar],28 R. Tsonaka, D. Rizopoulos, and E. Lesaffre, Power and sample size calculations for discrete bounded outcome scores, Stat. Med. 25 (2006), pp. 4241–4252. doi: 10.1002/sim.2679[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] to a joint modeling setting. Our approach is illustrated on longitudinal profiles of multiple patients’ reported outcomes to predict the current clinical status of rheumatoid arthritis patients by a disease activities score of 28 joints (DAS28). Both a maximum likelihood as well as a Bayesian approach is developed.     

Testing for sphericity in a two-way error components panel data model

This article is concerned with sphericity test for the two-way error components panel data model. It is found that the John statistic and the bias-corrected LM statistic recently developed by Baltagi et al. (2011 Baltagi, B. H., Feng, Q., Kao, C. (2011). Testing for sphericity in a fixed effects panel data model. Econometrics Journal 14:25–47.[Crossref], [Web of Science ®] , [Google Scholar])Baltagi et al. (2012 Baltagi, B. H., Feng, Q., Kao, C. (2012). A Lagrange multiplier test for cross-sectional dependence in a fixed effects panel data model. Journal of Econometrics 170:164–177.[Crossref], [Web of Science ®] , [Google Scholar], which are based on the within residuals, are not helpful under the present circumstances even though they are in the one-way fixed effects model. However, we prove that when the within residuals are properly transformed, the resulting residuals can serve to construct useful statistics that are similar to those of Baltagi et al. (2011 Baltagi, B. H., Feng, Q., Kao, C. (2011). Testing for sphericity in a fixed effects panel data model. Econometrics Journal 14:25–47.[Crossref], [Web of Science ®] , [Google Scholar])Baltagi et al. (2012 Baltagi, B. H., Feng, Q., Kao, C. (2012). A Lagrange multiplier test for cross-sectional dependence in a fixed effects panel data model. Journal of Econometrics 170:164–177.[Crossref], [Web of Science ®] , [Google Scholar]). Simulation results show that the newly proposed statistics perform well under the null hypothesis and several typical alternatives.     

A stratified unrelated question randomized response model using Neyman allocation

This paper applies stratified random sampling using Neyman allocation to Mangat et al. (1992 Mangat, N.S., Singh, R., Singh, S. (1992). An improved unrelated question randomized response strategy. Cal. Stat. Assoc. Bull. 42:277–281.[Crossref] , [Google Scholar]) unrelated question randomized response (RR) strategy for both completely truthful reporting and less than completely truthful reporting. It is shown that, for the prior information given, our new model is more efficient in terms of variance (in the case of completely truthful reporting) and mean square error (in terms of less than completely truthful reporting) than Kim and Elam's (2007 Kim, J.M., Elam, M.E. (2007). A stratified unrelated question randomized response model. Stat. Papers 48:215–233.[Crossref], [Web of Science ®] , [Google Scholar]) model. Numerical illustrations and graphs are also given in support of the present study.     

Random Effects,Fixed Effects and Hausman's Test for the Generalized Mixed Regressive Spatial Autoregressive Panel Data Model

This article suggests random and fixed effects spatial two-stage least squares estimators for the generalized mixed regressive spatial autoregressive panel data model. This extends the generalized spatial panel model of Baltagi et al. (2013 Baltagi, B. H., Egger, P., Pfaffermayr, M. (2013). A generalized spatial panel data model with random effects. Econometric Reviews 32:650–685.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) by the inclusion of a spatial lag term. The estimation method utilizes the Generalized Moments method suggested by Kapoor et al. (2007 Kapoor, M., Kelejian, H. H., Prucha, I. R. (2007). Panel data models with spatially correlated error components. Journal of Econometrics 127(1):97–130.[Crossref], [Web of Science ®] , [Google Scholar]) for a spatial autoregressive panel data model. We derive the asymptotic distributions of these estimators and suggest a Hausman test a la Mutl and Pfaffermayr (2011 Mutl, J., Pfaffermayr, M. (2011). The Hausman test in a Cliff and Ord panel model. Econometrics Journal 14:48–76.[Crossref], [Web of Science ®] , [Google Scholar]) based on the difference between these estimators. Monte Carlo experiments are performed to investigate the performance of these estimators as well as the corresponding Hausman test.     

Empirical Likelihood in Causal Inference

This paper discusses the estimation of average treatment effects in observational causal inferences. By employing a working propensity score and two working regression models for treatment and control groups, Robins et al. (1994 Robins , J. M. , Rotnitzky , A. , Zhao , L. P. ( 1994 ). Estimation of regression coefficients when some regressors are not always observed . Journal of the American Statistical Association 89 : 846 – 866 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], 1995 Robins , J. M. , Rotnitzky , A. , Zhao , L. P. ( 1995 ). Analysis of semiparametric regression models for repeated outcomes in the presence of missing data . Journal of the American Statistical Association 90 : 106 – 121 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) introduced the augmented inverse probability weighting (AIPW) method for estimation of average treatment effects, which extends the inverse probability weighting (IPW) method of Horvitz and Thompson (1952 Horvitz , D. G. , Thompson , D. J. ( 1952 ). A generalization of sampling without replacement from a finite universe . Journal of the American Statistical Association 47 : 663 – 685 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]); the AIPW estimators are locally efficient and doubly robust. In this paper, we study a hybrid of the empirical likelihood method and the method of moments by employing three estimating functions, which can generate estimators for average treatment effects that are locally efficient and doubly robust. The proposed estimators of average treatment effects are efficient for the given choice of three estimating functions when the working propensity score is correctly specified, and thus are more efficient than the AIPW estimators. In addition, we consider a regression method for estimation of the average treatment effects when working regression models for both the treatment and control groups are correctly specified; the asymptotic variance of the resulting estimator is no greater than the semiparametric variance bound characterized by the theory of Robins et al. (1994 Robins , J. M. , Rotnitzky , A. , Zhao , L. P. ( 1994 ). Estimation of regression coefficients when some regressors are not always observed . Journal of the American Statistical Association 89 : 846 – 866 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], 1995 Robins , J. M. , Rotnitzky , A. , Zhao , L. P. ( 1995 ). Analysis of semiparametric regression models for repeated outcomes in the presence of missing data . Journal of the American Statistical Association 90 : 106 – 121 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). Finally, we present a simulation study to compare the finite-sample performance of various methods with respect to bias, efficiency, and robustness to model misspecification.     

On the optimal allocation of active redundancies in series system

This paper studies the allocations of two non identical active redundancies in series systems in terms of the reversed hazard rate order and hazard rate order, which generalizes some results built in Valdés and Zequeira (2003 Valdés, J. E., and R. I. Zequeira 2003. On the optimal allocation of an active redundancy in a two-component series system. Stat. Probab. Lett. 63:325–32.[Crossref], [Web of Science ®] , [Google Scholar], 2006 Valdés, J. E., and R. I. Zequeira 2006. On the optimal allocation of two active redundancies in a two-component series system. Oper. Res. Lett. 34:49–52.[Crossref], [Web of Science ®] , [Google Scholar]).     

A Bayesian control chart for a common coefficient of variation

By using the medical data analyzed by Kang et al. (2007 Kang, C.W., Lee, M.S., Seong, Y.J., Hawkins, D.M. (2007). A control chart for the coefficient of variation. J. Qual. Technol. 39(2):151–158.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), a Bayesian procedure is applied to obtain control limits for the coefficient of variation. Reference and probability matching priors are derived for a common coefficient of variation across the range of sample values. By simulating the posterior predictive density function of a future coefficient of variation, it is shown that the control limits are effectively identical to those obtained by Kang et al. (2007 Kang, C.W., Lee, M.S., Seong, Y.J., Hawkins, D.M. (2007). A control chart for the coefficient of variation. J. Qual. Technol. 39(2):151–158.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) for the specific dataset they used. This article illustrates the flexibility and unique features of the Bayesian simulation method for obtaining posterior distributions, predictive intervals, and run-lengths in the case of the coefficient of variation. A simulation study shows that the 95% Bayesian confidence intervals for the coefficient of variation have the correct frequentist coverage.     

Some extensions of circular balanced and circular strongly balanced repeated measurements designs

Repeated measurement designs are widely used in medicine, pharmacology, animal sciences, and psychology. In this paper the works of Iqbal and Tahir (2009 Iqbal, I., and M. H. Tahir. 2009. Circular strongly balanced repeated measurements designs. Communications in Statistics—Theory and Methods 38:3686–96.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and Iqbal, Tahir, and Ghazali (2010 Iqbal, I., M. H. Tahir, and S. S. A. Ghazali. 2010. Circular first- and second-order balanced repeated measurements designs. Communications in Statistics—Theory and Methods 39:228–40.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) are generalized for the construction of circular-balanced and circular strongly balanced repeated measurements designs through the method of cyclic shifts for three periods.     

Improved Exponential Type Estimators of the Mean of a Sensitive Variable in the Presence of Nonsensitive Auxiliary Information

Recently, Koyuncu et al. (2013 Koyuncu, N., Gupta, S., Sousa, R. (2014). Exponential type estimators of the mean of a sensitive variable in the presence of non-sensitive auxiliary information. Communications in Statistics- Simulation and Computation[PubMed], [Web of Science ®] , [Google Scholar]) proposed an exponential type estimator to improve the efficiency of mean estimator based on randomized response technique. In this article, we propose an improved exponential type estimator which is more efficient than the Koyuncu et al. (2013 Koyuncu, N., Gupta, S., Sousa, R. (2014). Exponential type estimators of the mean of a sensitive variable in the presence of non-sensitive auxiliary information. Communications in Statistics- Simulation and Computation[PubMed], [Web of Science ®] , [Google Scholar]) estimator, which in turn was shown to be more efficient than the usual mean estimator, ratio estimator, regression estimator, and the Gupta et al. (2012 Gupta, S., Shabbir, J., Sousa, R., Corte-Real, P. (2012). Regression estimation of the mean of a sensitive variable in the presence of auxiliary information. Communications in Statistics – Theory and Methods 41:2394–2404.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) estimator. Under simple random sampling without replacement (SRSWOR) scheme, bias and mean square error expressions for the proposed estimator are obtained up to first order of approximation and comparisons are made with the Koyuncu et al. (2013 Koyuncu, N., Gupta, S., Sousa, R. (2014). Exponential type estimators of the mean of a sensitive variable in the presence of non-sensitive auxiliary information. Communications in Statistics- Simulation and Computation[PubMed], [Web of Science ®] , [Google Scholar]) estimator. A simulation study is used to observe the performances of these two estimators. Theoretical findings are also supported by a numerical example with real data. We also show how to, extend the proposed estimator to the case when more than one auxiliary variable is available.     

A two-stage Land et al.'s randomized response model for estimating a rare sensitive attribute using Poisson distribution

The crux of this paper is to estimate the mean of the number of persons possessing a rare sensitive attribute based on the Mangat (1992 Mangat, N.S. (1992). Two stage reandomized response sampling procedure using unrelated question. J. Ind. Soc. Agric. Stat. 44(1):82–87. [Google Scholar]) randomization device by utilizing the Poisson distribution in survey sampling. It is shown that the proposed model is more efficient than Land et al. (2011 Land, M., Singh, S., Sedory, S.A. (2011). Estimation of a rare attribute using Poisson distribution. Statistics doi:10.1080/02331888.2010.524300[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) when the proportion of persons possessing a rare unrelated attribute is known. Properties of the proposed randomized response model have been studied along with recommendations. We have also extended the proposed model to stratified random sampling on the lines of Lee et al. (2013 Lee, G.S., Uhm, D., Kim, J.M. (2013). Estimation of a rare sensitive attribute in stratified sampling using Poisson distribution. Statistics 47(3):575–589.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). It has been also shown that the proposed estimator is better than Lee et al.'s (2013 Lee, G.S., Uhm, D., Kim, J.M. (2013). Estimation of a rare sensitive attribute in stratified sampling using Poisson distribution. Statistics 47(3):575–589.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) estimator. Numerical illustrations are also given in support of the present study.     

Characterization results based on dynamic Tsallis cumulative residual entropy

In this article, the concept of cumulative residual entropy (CRE) given by Rao et al. (2004 Rao, M., Chen, Y., Vemuri, B.C., Wang, F. (2004). Cumulative residual entropy: A new measure of information. IEEE Trans. Inf. Theory 50:1220–1228.[Crossref], [Web of Science ®] , [Google Scholar]) is extended to Tsallis entropy function and dynamic version, both residual and past of it. We study some properties and characterization results for these generalized measures. In addition, we provide some characterization results of the first-order statistic based on the Tsallis survival entropy.     

A Modification of a Percentile Estimation Procedure Based on Generalized Polya Urns

Adaptive designs find an important application in the estimation of unknown percentiles for an underlying dose-response curve. A nonparametric adaptive design was suggested by Mugno et al. (2004 Mugno, R.A., Zhus, W., Rosenberger, W.F. (2004). Adaptive urn designs for estimating several percentiles of a dose-response curve. Statist. Med. 23(13):2137–2150.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) to simultaneously estimate multiple percentiles of an unknown dose-response curve via generalized Polya urns. In this article, we examine the properties of the design proposed by Mugno et al. (2004 Mugno, R.A., Zhus, W., Rosenberger, W.F. (2004). Adaptive urn designs for estimating several percentiles of a dose-response curve. Statist. Med. 23(13):2137–2150.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) when delays in observing responses are encountered. Using simulations, we evaluate a modification of the design under varying group sizes. Our results demonstrate unbiased estimation with minimal loss in efficiency when compared to the original compound urn design.     

Buffered Autoregressive Models With Conditional Heteroscedasticity: An Application to Exchange Rates

This article introduces a new model called the buffered autoregressive model with generalized autoregressive conditional heteroscedasticity (BAR-GARCH). The proposed model, as an extension of the BAR model in Li et al. (2015 Li, G.D., Guan, B., Li, W.K., and Yu, P. L.H. (2015), “Hysteretic Autoregressive Time Series Models,” Biometrika, 102, 717–723.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), can capture the buffering phenomena of time series in both the conditional mean and variance. Thus, it provides us a new way to study the nonlinearity of time series. Compared with the existing AR-GARCH and threshold AR-GARCH models, an application to several exchange rates highlights the importance of the BAR-GARCH model.