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.     

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.     

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.     

An Approximation Model of the Collective Risk Model with INAR(1) Claim Process

Cossette et al. (2010 Cossette, H., Marceau, E., Maume-Deschamps, V. (2010). Discerte-time risk models based on time series for count random variables. ASTIN Bull. 40:123–150.[Crossref], [Web of Science ®] , [Google Scholar], 2011 Cossette, H., Marceau, E., Toureille, F. (2011). risk models based on time series for count random variables. Insur. Math. Econ. 48:19–28.[Crossref], [Web of Science ®] , [Google Scholar]) gave a novel collective risk model where the total numbers of claims satisfy the first-order integer-valued autoregressive process. For a risk model, it is interesting to investigate the upper bound of ruin probability. However, the loss increments of the above model are dependent; it is difficult to derive the upper bound of ruin probability. In this article, we propose an approximation model with stationary independent increments. The upper bound of ruin probability and the adjustment coefficient are derived. The approximation model is illustrated via four simulated examples. Results show that the gap of the approximation model and dependent model can be ignored by adjusting values of parameters.     

An Efficient Class of Estimators for the Population Mean Using Auxiliary Information in Stratified Random Sampling

This article addresses the problem of estimating the population mean in stratified random sampling using the information of an auxiliary variable. A class of estimators for population mean is defined with its properties under large sample approximation. In particular, various classes of estimators are identified as particular member of the suggested class. It has been shown that the proposed class of estimators is better than usual unbiased estimator, usual combined ratio estimator, usual product estimator, usual regression estimator and Koyuncu and Kadilar (2009 Koyuncu, N., Kadilar, C. (2009). Ratio and product estimators in stratified random sampling. J. Statist. Plan. Infere. 139:2552–2558.[Crossref], [Web of Science ®] , [Google Scholar]) class of estimators. The results have been illustrated through an empirical study.     

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.     

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.     

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.     

A local moment type estimator for an extreme quantile in regression with random covariates

A conditional extreme quantile estimator is proposed in the presence of random covariates. It is based on an adaptation of the moment estimator introduced by Dekkers et al. (1989 Dekkers, A.L.M., Einmahl, J.H.J., de Haan, L. (1989). A moment estimator for the index of an extreme-value distribution. Ann. Statist. 17:1833–1855.[Crossref], [Web of Science ®] , [Google Scholar]) in the classical univariate setting, and thus it is valid in the domain of attraction of the extreme value distribution, i.e., whatever the sign of the extreme value index is. Asymptotic normality of the estimator is established under suitable assumptions, and its finite sample behavior is evaluated with a small simulation study, where a comparison with an alternative estimator already proposed in the literature is provided. An illustration to a real dataset concerning the world catalogue of earthquake magnitudes is also proposed.     

The raise estimator estimation,inference, and properties

Several methods using different approaches have been developed to remedy the consequences of collinearity. To the best of our knowledge, only the raise estimator proposed by García et al. (2010 García, C.B., García, J., Soto, J. (2010). The raise method: An alternative procedure to estimate the parameters in presence of collinearity. Qual. Quantity 45(2):403–423.[Crossref], [Web of Science ®] , [Google Scholar]) deals with this problem from a geometric perspective. This article fully develops the raise estimator for a model with two standardized explanatory variables. Inference in the raise estimator is examined, showing that it can be obtained from ordinary least squares methodology. In addition, contrary to what happens in ridge regression, the raise estimator maintains the coefficient of determination value constant. The expression of the variance inflation factor for the raise estimator is also presented. Finally, a comparative study of the raise and ridge estimators is carried out using an example.     

Comment on a generalized stochastic restricted ridge regression estimator

In this note, we make some comments about the paper of Alheety and Kibria (2014 Alheety, M.I., Kibria, B.M.G. (2014). A generalized stochastic restricted ridge regression estimator. Commun. Stat. Theor. Meth. 43:4415–4427.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and correct the wrongly proved Theorems in that paper.     

Confidence bands for the logistic and probit regression models over intervals

This article presents methods for the construction of two-sided and one-sided simultaneous hyperbolic bands for the logistic and probit regression models when the predictor variable is restricted to a given interval. The bands are constructed based on the asymptotic properties of the maximum likelihood estimators. Past articles have considered building two-sided asymptotic confidence bands for the logistic model, such as Piegorsch and Casella (1988 Piegorsch, W.W., Casella, G. (1988). Confidence bands for logistic regression with restricted predictor variables. Biometrics 44:739–750.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). However, the confidence bands given by Piegorsch and Casella are conservative under a single interval restriction, and it is shown in this article that their bands can be sharpened using the methods proposed here. Furthermore, no method has yet appeared in the literature for constructing one-sided confidence bands for the logistic model, and no work has been done for building confidence bands for the probit model, over a limited range of the predictor variable. This article provides methods for computing critical points in these areas.     

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.     

Quantile-based Chernoff distance for truncated random variables

Several probability distributions such as power-Pareto distribution (see Gilchrist 2000 Gilchrist, W. 2000. Statistical modelling with quantile functions. Boca Raton, FL: Chapman and Hall/CRC.[Crossref] , [Google Scholar] and Hankin and Lee 2006 Hankin, R. K. S., and A. Lee. 2006. A new family of non-negative distributions. Australian and New Zealand Journal of Statistics 48:67–78.[Crossref], [Web of Science ®] , [Google Scholar]), various forms of lambda distributions (see Ramberg and Schmeiser 1974 Ramberg, J. S., and B. W. Schmeiser. 1974. An appropriate method for generating asymmetric random variables. Communications of the ACM 17:78–82.[Crossref], [Web of Science ®] , [Google Scholar] and Freimer et al. 1988 Freimer, M., S. Mudholkar, G. Kollia, and C. T. Lin. 1988. A study of the generalized lambda family. Communications in Statistics - Theory and Methods 17:3547–67.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Govindarajulu distribution (see Nair, Sankaran, and Vineshkumar 2012 Nair, U. N., P. G. Sankaran, and B. Vineshkumar. 2012. The Govindarajulu distribution: some properties and applications. Communications in Statistics—Theory and Methods 41:4391–406.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), etc., do not have manageable distribution functions, though they have tractable quantile functions. Hence, analytical study of the properties of Chernoff distance of two random variables associated with these distributions via traditional distribution function-based tool becomes difficult. To make this simple, in this paper, we introduce quantile-based Chernoff distance for (left or right) truncated random variables and study its various properties. Some useful bounds as well as characterization results are obtained.     

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.     

Complete and complete moment convergence for i.i.d. random variables under exponential moment conditions

In this paper, we establish a complete convergence result and a complete moment convergence result for i.i.d. random variables under moment condition which is slightly weaker than the existence of the moment generating function. The main results extend and improve the related known results of Lanzinger (1998 Lanzinger, H. (1998). A Baum-Katz theorem for random variables under exponential moment conditions. Stat. Probab. Lett. 39(2):89–95.[Crossref], [Web of Science ®] , [Google Scholar]) and Gut and Stadtmüller (2011 Gut, A., Stadtmüller, U. (2011). An intermediate Baum-Katz theorem. Stat. Probab. Lett. 81(10):1486–1492.[Crossref], [Web of Science ®] , [Google Scholar]).     

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.     

On the comparison of Warner's and unrelated question randomized response plans for estimating sensitive finite population proportions

We consider the problem of estimation of a finite population proportion (P) related to a sensitive attribute under Warner's (1965 Warner, S.L. (1965). Randomized response: A survey technique for eliminating evasive answer bias. J. Am. Stat. Assoc. 60:63–69.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) randomized response plan and the unrelated question plan due to Horvitz et al. (1967 Warner, S.L. (1965). Randomized response: A survey technique for eliminating evasive answer bias. J. Am. Stat. Assoc. 60:63–69.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and prove that for a given probability sampling design, given any linear unbiased estimator (LUE) of P based on Warner's (1965 Warner, S.L. (1965). Randomized response: A survey technique for eliminating evasive answer bias. J. Am. Stat. Assoc. 60:63–69.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) plan with any given value of the plan parameter, there exists an LUE of P based on the unrelated question plan with a uniformly smaller variance for suitable choices of the plan parameters. Assuming that only the attribute is sensitive but its complement is innocuous, the same is also shown to be true when the plan parameters for the two plans are so chosen so that both offer the same specified level of privacy.     

A Realized Stochastic Volatility Model With Box–Cox Transformation

This article presents a new class of realized stochastic volatility model based on realized volatilities and returns jointly. We generalize the traditionally used logarithm transformation of realized volatility to the Box–Cox transformation, a more flexible parametric family of transformations. A two-step maximum likelihood estimation procedure is introduced to estimate this model on the basis of Koopman and Scharth (2013 Koopman, S.J., Scharth, M. (2013), The Analysis of Stochastic Volatility in the Presence of Daily Realised Measures, Journal of Financial Econometrics, 11, 76–115.[Crossref], [Web of Science ®] , [Google Scholar]). Simulation results show that the two-step estimator performs well, and the misspecified log transformation may lead to inaccurate parameter estimation and certain excessive skewness and kurtosis. Finally, an empirical investigation on realized volatility measures and daily returns is carried out for several stock indices.     

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.