A Comparative Note about Estimation of the Fractional Parameter under Additive Outliers

In recent articles, Fajardo et al. (2009 Fajardo Molinares, F., Reisen, V.A., Cribari-Neto, F. (2009). Robust estimation in long-memory processes under additive outliers. Journal of Statistical Planning and Inference 139:2511–2525.[Crossref], [Web of Science ®] , [Google Scholar]) and Reisen and Fajardo (2012) propose an alternative semiparametric estimator of the fractional parameter in ARFIMA models which is robust to the presence of additive outliers. The results are very interesting, however, they use samples of 300 or 800 observations which are rarely found in macroeconomics. In order to perform a comparison, I estimate the fractional parameter using the procedure of Geweke and Porter-Hudak (1983 Geweke, J., Porter-Hudak, S. (1983). The estimation and application of long memory time series model. Journal of Time Series Analysis 4:221–238.[Crossref] , [Google Scholar]) augmented with dummy variables associated with the (previously) detected outliers using the statistic τ_d suggested by Perron and Rodríguez (2003 Perron, P., Rodríguez, G. (2003). Searching for additive outliers in nonstationary time series. Journal of Time Series Analysis 24(2):193–220.[Crossref], [Web of Science ®] , [Google Scholar]). Comparing with Fajardo et al. (2009 Fajardo Molinares, F., Reisen, V.A., Cribari-Neto, F. (2009). Robust estimation in long-memory processes under additive outliers. Journal of Statistical Planning and Inference 139:2511–2525.[Crossref], [Web of Science ®] , [Google Scholar]) and Reisen and Fajardo (2012), I found better results for the mean and bias of the fractional parameter when T = 100 and the results in terms of the standard deviation and the MSE are very similar. However, for higher sample sizes such as 300 or 800, the robust procedure performs better. Empirical applications for seven monthly Latin-American inflation series with very small sample sizes contaminated by additive outliers are discussed.     

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.     

Analysis of Order Statistics from Distributions with Regularly Varying Tails

In this article, necessary conditions for comparing order statistics from distributions with regularly varying tails are discussed in terms of various stochastic orders. A necessary and sufficient condition for stochastically comparing tail behaviors of order statistics is derived. The main results generalize and recover some results in Kleiber (2002 Kleiber, C. (2002). Variability ordering of heavy-tailed distributions with applications to order statistics. Statist. Probab. Lett. 58:381388.[Crossref], [Web of Science ®] , [Google Scholar], 2004 Kleiber, C. (2004). Lorenz ordering of order statistics from log-logistic and related distributions. J. Statist. Plann. Infer. 120:2004.[Crossref], [Web of Science ®] , [Google Scholar]). Extensions to coherent systems are mentioned as well.     

Bayesian Estimation for Linear Functions of Poisson Rates

The probability matching prior for linear functions of Poisson parameters is derived. A comparison is made between the confidence intervals obtained by Stamey and Hamilton (2006 Stamey, J., Hamilton, C. (2006). A note on confidence intervals for a linear function of Poisson rates. Commun. Statist. Simul. &; Computat. 35(4):849–856.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), and the intervals derived by us when using the Jeffreys’ and probability matching priors. The intervals obtained from the Jeffreys’ prior are in some cases fiducial intervals (Krishnamoorthy and Lee, 2010 Krishnamoorthy, K., Lee, M. (2010). Inference for functions of parameters in discrete distributions based on fiducial approach: Binomial and Poisson cases. J. Statist. Plann. Infere. 140(5):1182–1192.[Crossref], [Web of Science ®] , [Google Scholar]). A weighted Monte Carlo method is used for the probability matching prior. The power and size of the test, using Bayesian methods, is compared to tests used by Krishnamoorthy and Thomson (2004 Krishnamoorthy, K., Thomson, J. (2004). A more powerful test for comparing two Poisson means. J. Statist. Plann. Infere. 119(1):23–35.[Crossref], [Web of Science ®] , [Google Scholar]). The Jeffreys’, probability matching and two other priors are used.     

Using the Inverse Maximum Ratio-Λ as a Technique to Quantify Surface Uniformity

Techniques used in variability assessment are subsequently used to draw conclusions regarding the “spread”/uniformity of data curves. Due to the limitations of these techniques, they are not adequate for circumstances where data manifest with multiple peaks. Examples of these manifestations (in three-dimensional space) include under-foot pressure distributions recorded for different types of footwear (Becerro-de-Bengoa-Vallejo et al., 2014 Biau, D.J. (2011). In brief: Standard deviation and standard error. Clinical Orthopaedics and Related Research 469(9):2661–2664.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Cibulka et al., 1994 Cibulka, M.T., Sinacore, D.R., Mueller, M.J. (1994). Shin splints and forefoot contact running: A case report. Journal of Orthopaedic &; Sports Physical Therapy 20(2):98–102.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Davies et al., 2003 Davies, M.B., Betts, R.P., Scott, I.R. (2003). Optical plantar pressure analysis following internal fixation for displaced intra-articular os calcis fractures. Foot &; Ankle International 24(11):851–856.[PubMed], [Web of Science ®] , [Google Scholar]), surface textures and interfaces designed to impact friction, and and and molecular surface structures such as viral epitopes (Torras and Garcia-Valls, 2004 Torras, C., Garcia-Valls, R. (2004). Quantification of membrane morphology by interpretation of scanning electron microscopy images. Journal of Membrane Science 233(1–2):119–127.[Crossref], [Web of Science ®] , [Google Scholar]; Pacejka, 1997; Fustaffson, 1997). This article proposes a technique for generating a single variable – Λ that will quantify the uniformity of such surfaces. We define and validate this technique using several mathematical and graphical models.     

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]).     

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.     

Bootstrap test of hypothesis for the multi-state models in survival analysis

Abstract

In the present paper we develop bootstrap tests of hypothesis, based on simulation, for the transition probability matrix arising in the context of a multi-state model. The bootstrap test statistic is based on the paper of Tattar and Vaman (2008 Tattar, P. N., Vaman, H. J. (2008). Testing transition probability matrix of a multi-state model with censored data. Lifetime Data Anal. 14(2):216–230.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), which develops a statistic for the testing problems concerning the transition probability matrix of the non homogeneous Markov process.     

Matrix mean squared error comparisons of some biased estimators with two biasing parameters

To deal with multicollinearity problem, the biased estimators with two biasing parameters have recently attracted much research interest. The aim of this article is to compare one of the last proposals given by Yang and Chang (2010 Yang, H., and X. Chang. 2010. A new two-parameter estimator in linear regression. Communications in Statistics: Theory and Methods 39 (6):923–34.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) with Liu-type estimator (Liu 2003 Liu, K. 2003. Using Liu-type estimator to combat collinearity. Communications in Statistics: Theory and Methods 32 (5):1009–20.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and k ? d class estimator (Sakallioglu and Kaciranlar 2008 Sakallioglu, S., and S. Kaciranlar. 2008. A new biased estimator based on ridge estimation. Statistical Papers 49:669–89.[Crossref], [Web of Science ®] , [Google Scholar]) under the matrix mean squared error criterion. As well as giving these comparisons theoretically, we support the results with the extended simulation studies and real data example, which show the advantages of the proposal given by Yang and Chang (2010 Yang, H., and X. Chang. 2010. A new two-parameter estimator in linear regression. Communications in Statistics: Theory and Methods 39 (6):923–34.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) over the other proposals with increasing multicollinearity level.     

Queues and Risk Processes with Dependencies

We study the generalization of the G/G/1 queue obtained by relaxing the assumption of independence between inter-arrival times and service requirements. The analysis is carried out for the class of multivariate matrix exponential distributions introduced in Ref.^[13 M. Bladt; B.F. Nielsen. Multivariate matrix-exponential distributions. Stochastic Models 2010, 26(1), 1–26.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]^]. In this setting, we obtain the steady-state waiting time distribution, and we show that the classical relation between the steady-state waiting time and workload distributions remains valid when the independence assumption is relaxed. We also prove duality results with the ruin functions in an ordinary and a delayed ruin process. These extend several known dualities between queueing and risk models in the independent case. Finally, we show that there exist stochastic order relations between the waiting times under various instances of correlation.     

General mathematical properties,regression and applications of the log-gamma-generated family

The construction of some wider families of continuous distributions obtained recently has attracted applied statisticians due to the analytical facilities available for easy computation of special functions in programming software. We study some general mathematical properties of the log-gamma-generated (LGG) family defined by Amini, MirMostafaee, and Ahmadi (2014 Amini, M., S. M. T. K. MirMostafaee, and J. Ahmadi. 2014. Log-gamma-generated families of distributions. Statistics 48:913–32.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). It generalizes the gamma-generated class pioneered by Risti? and Balakrishnan (2012 Risti?, M. M., and N. Balakrishnan. 2012. The gamma exponentiated exponential distribution. Journal of Statistical Computation and Simulation 82:1191–206.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). We present some of its special models and derive explicit expressions for the ordinary and incomplete moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves, Shannon entropy, Rényi entropy, reliability, and order statistics. Models in this family are compared with nested and non nested models. Further, we propose and study a new LGG family regression model. We demonstrate that the new regression model can be applied to censored data since it represents a parametric family of models and therefore can be used more effectively in the analysis of survival data. We prove that the proposed models can provide consistently better fits in some applications to real data sets.     

On Complete Convergence for Weighted Sums of NA Random Fields

In this paper, we prove the complete convergence for the weighted sums of negatively associated random variables with multidimensional indices. The main result generalizes Theorem 2.1 in Kuczmaszewska and Lagodowski (2011 Kuczmaszewska, A., Lagodowski, Z.A. (2011). Convergence rates in the SLLN for some classes of dependent random field. J. Math. Anal. Appl. 380:571–584.[Crossref], [Web of Science ®] , [Google Scholar]) to the case of weighted sums.     

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.     

Bahadur Representation of Linear Kernel Quantile Estimator for Stationary Processes

In this article, we discuss the method of linear kernel quantile estimator proposed by Parzen (1979 Parzen, E. (1979). Nonparametric statistical data modeling. J. Amer. Statist. Assoc. 74:105121.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). We establish a Bahadur representation in sense of almost surely convergence with the rate log^{? α}n under the case of S-mixing random variable sequence which was proposed by Berkes (2009 Berkes, I., Hörmann, S., (2009). Asymptotic results for the itpirical process of stationary sequences. Stoch. Process. Their Applic. 119:12981324.[Crossref], [Web of Science ®] , [Google Scholar]). We also obtain the strong consistence of this estimator and its convergence rate.     

Adjusted Confidence Bands for Complex Survey Data

Confidence bands in nonparametric regression have been studied for a long time with data assumed to be generated from independent and identically distributed (iid) random variables. The methods and theoretical results for iid data, however, do not directly apply to data from stratified multistage samples. In this paper, we extend the confidence bands introduced by Zhang and Lu (2008 Zhang, G., Lu, Y. (2008). Adjusted confidence bands in nonparametric regression. Communications in Statistics-Simulation and Computation 37: 106–113.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) for iid case to complex surveys based on an entirely data-driven procedure; the proposed confidence bands incorporate both the sampling weights and the kernel weights. Simulation studies show that the proposed method works well.     

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.     

Bimodal symmetric-asymmetric power-normal families

This article proposes new symmetric and asymmetric distributions applying methods analogous as the ones in Kim (2005 Kim, H.J. (2005). On a class of two-piece skew-normal distributions. Statist.: J. Theoret. Appl. Statist. 39:537–553.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and Arnold et al. (2009 Arnold, B.C., H.W. Gómez, and H.S. Salinas. (2009). On multiple constraint skewed models. Statist. J. Theoret. Appl. Statist. 43: 279–293.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) to the exponentiated normal distribution studied in Durrans (1992 Durrans, S.R. (1992). Distributions of fractional order statistics in hydrology. Water Resour. Res. 28:1649–1655.[Crossref], [Web of Science ®] , [Google Scholar]), that we call the power-normal (PN) distribution. The proposed bimodal extension, the main focus of the paper, is called the bimodal power-normal model and is denoted by BPN(α) model, where α is the asymmetry parameter. The authors give some properties including moments and maximum likelihood estimation. Two important features of the model proposed is that its normalizing constant has closed and simple form and that the Fisher information matrix is nonsingular, guaranteeing large sample properties of the maximum likelihood estimators. Finally, simulation studies and real applications reveal that the proposed model can perform well in both situations.     

Test of Independence for Baker’s Bivariate Distributions

Baker (2008 Baker, R. (2008). An order-statistics-based method for constructing multivariate distributions with fixed marginals. Journal of Multivariate Analysis 99: 2312–2327.[Crossref], [Web of Science ®] , [Google Scholar]) introduced a new method for constructing multivariate distributions with given marginals based on order statistics. In this paper, we provide a test of independence for a pair of absolutely continuous random variables (X, Y) jointly distributed according to Baker’s bivariate distributions. Our purpose is to test the hypothesis that X and Y are independent versus the alternative that X and Y are positively (negatively) quadrant dependent. The asymptotic distribution of the proposed test statistic is investigated. Also, the powers of the proposed test and the class of distribution-free tests proposed by Kochar and Gupta (1987 Kochar, S. G., Gupta, R. P. (1987). Competitors of Kendall-tau test for testing independence against positive quadrant dependence. Biometrika 74(3): 664–666.[Crossref], [Web of Science ®] , [Google Scholar]) are compared empirically via a simulation study.     

Nonparametric Inference for an Inverse-Probability-Weighted Estimator with Doubly Truncated Data

Efron and Petrosian (1999 Efron, B., Petrosian, V. (1999). Nonparametric methods for doubly truncated data. Journal of the American Statistical Association 94:824–834.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) formulated the problem of double truncation and proposed nonparametric methods on testing and estimation. An alternative estimation method was proposed by Shen (2010a Shen, P.S. (2010a). Nonparametric analysis of doubly truncated data. Annals of the Institute of Statistical Mathematics 62:835–853.[Crossref], [Web of Science ®] , [Google Scholar]), utilizing the inverse-probability-weighting technique. One aim of this paper was to assess the computational complexity of the existing estimation methods. Through a simulation study, we found that these two estimation methods have the same level of computational efficiency. The other aim was to study the noniterative IPW estimator under the condition that truncation variables are independent. The IPW estimator and the interval estimation was proved satisfactory in the simulation study.     

On the Optimality of Circular Block Designs Under a Mixed Interference Model

Filipiak and Markiewicz (2012 Filipiak, K., Markiewicz, A. (2012). On universal optimality of circular weakly neighbor balanced designs under an interference model. Comm. Stat. Theor Methods 41: 2356–2366.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) proved the universal optimality of circular weakly neighbor balanced designs (CWNBDs) under the interference model with fixed neighbor effects among the class of complete block designs. In two special cases where a CWNBD cannot exist, Filipiak et al. (2012 Filipiak, K., Markiewicz, A., Ró?ański, R. (2012). Maximal determinant over a certain class of matrices and its application to D-optimality of designs. Linear Algebra Appl. 436(4): 874–887.[Crossref], [Web of Science ®] , [Google Scholar]) characterized D-optimal designs. The aim of this paper is to show the universal optimality of CWNBDs and to characterize D-optimal designs under the interference model with random neighbor effects.