Stochastic Comparison on General Inactivity Time and General Residual Life of k-Out-of-n Systems

This paper conducts stochastic comparison on general residual life and general inactivity time of (n ? k + 1)-out-of-n systems and investigates the stochastic behavior of the general inactivity time of a system with units having decreasing reversed hazard rate. These results strengthen some conclusions in both Khaledi and Shaked (2006 Khaledi , B. , Shaked , M. ( 2006 ). Ordering conditional residual lifetimes of coherent systems . Journal of Statistical Planning and Inference 137 : 1173 – 1184 .[Crossref], [Web of Science ®] , [Google Scholar]) and Hu et al. (2007 Hu , T. , Jin , W. , Khaledi , M. ( 2007 ). Ordering conditional distributions of generalized order statistics . Probability in the Engineering and Informational Sciences 21 : 401 – 417 .[Crossref], [Web of Science ®] , [Google Scholar]).     

Is Each NPMLE of a Continuous Bivariate Distribution Function with Singly Right-Censored Data Really Inconsistent?

We consider non-parametric estimation of a continuous cdf of a random vector (X ₁, X ₂). With bivariate RC data, it is stated in van der Laan (1996 Van der Laan , M. J. ( 1996 ) Efficient estimation in the bivariate censoring model and repairing NPMLE . Ann. Statist. 24 : 596 – 627 .[Crossref], [Web of Science ®] , [Google Scholar], p. 598¹⁰, Ann. Statist.), Quale et al. (2006 Quale , C. M. , van der Laan , M. J. , Robins , J. R. ( 2006 ). Locally efficient estimation with bivariate right-censored data . JASA. 101 : 1076 – 1084 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar], JASA) etc. that “it is well known that the NPMLE for continuous data is inconsistent (Tsai et al. (1986 Tsai , W. Y. , Leurgans , S. , Crowley , J. ( 1986 ). Nonparametric estimation of a bivariate survival function in the presence of censoring . Ann. Statist. 14 : 1351 – 1365 .[Crossref], [Web of Science ®] , [Google Scholar])).” The claim is based on a result in Tsai et al. (1986 Tsai , W. Y. , Leurgans , S. , Crowley , J. ( 1986 ). Nonparametric estimation of a bivariate survival function in the presence of censoring . Ann. Statist. 14 : 1351 – 1365 .[Crossref], [Web of Science ®] , [Google Scholar], p.1352, Ann. Statist.) that if X ₁ is right censored but not X ₂, then common ways for defining one NPMLE lead to inconsistency. If X ₁ is right censored and X ₂ is type I right-censored (which includes the case in Tsai et al.), we present a consistent NPMLE. The result corrects a common misinterpretation of Tsai's example (Tsai et al., 1986 Tsai , W. Y. , Leurgans , S. , Crowley , J. ( 1986 ). Nonparametric estimation of a bivariate survival function in the presence of censoring . Ann. Statist. 14 : 1351 – 1365 .[Crossref], [Web of Science ®] , [Google Scholar], Ann. Statist.).     

A Comparison of Procedures for Controlling the False Discovery Rate in the Presence of Small Variance Genes: A Simulation Study

The Significance Analysis of Microarrays (SAM; Tusher et al., 2001 Tusher , V. G. , Tibshirani , R. , Chu , G. ( 2001 ). Significance analysis of microarrys applied to the ionizing radiation response . Proceedings of the National Academy of Sciences 98 : 5116 – 5121 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) method is widely used in analyzing gene expression data while controlling the FDR by using resampling-based procedure in the microarray setting. One of the main components of the SAM procedure is the adjustment of the test statistic. The introduction of the fudge factor to the test statistic aims at deflating the large value of test statistics due to the small standard error of gene-expression. Lin et al. (2008 Lin , D. , Shkedy , Z. , Burzykowski , T. , Göhlmann , H. W. H. , De Bondt , A. , Perera , T. , Geerts , T. , Bijnens , L. ( 2008 ). Significance analysis of microarray (SAM) for comparisons of several treatments with one control . Biometric Journal, MCP 50 ( 5 ): 801 – 823 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) pointed out that the fudge factor does not effectively improve the power and the control of the FDR as compared to the SAM procedure without the fudge factor in the presence of small variance genes. Motivated by the simulation results presented in Lin et al. (2008 Lin , D. , Shkedy , Z. , Burzykowski , T. , Göhlmann , H. W. H. , De Bondt , A. , Perera , T. , Geerts , T. , Bijnens , L. ( 2008 ). Significance analysis of microarray (SAM) for comparisons of several treatments with one control . Biometric Journal, MCP 50 ( 5 ): 801 – 823 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), in this article, we extend our study to compare several methods for choosing the fudge factor in the modified t-type test statistics and use simulation studies to investigate the power and the control of the FDR of the considered methods.     

Regression M-estimators with One Modified Form of Doubly Censored Data

In this article, we consider the M-estimators for the linear regression model when both response and covariate variables are subject to double censoring. The proposed estimators are constructed as some functional of three types of estimators for a bivariate survival distribution. The first two estimators are the generalizations of the Campbell and Földes (1982 Campbell, G. and Földes, A. 1982. “Large sample properties of nonparametric statistical inference”. In Nonparametric Statistical Inference., Edited by: Gnredenko, B. V., Puri, M. L. and Vineze, I. 103–122. Amsterdam: North-Holland.  [Google Scholar]) and Dabrowska (1988 Dabrowska, D. M. 1988. Kaplan-Meier estimate on the plane. Annals of Statistics, 18: 1475–1489. [Crossref], [Web of Science ®] , [Google Scholar]) estimators proposed by Shen (2009 Shen, P. S. 2009. Nonparametric estimation of the bivariate survival function one modified form of doubly censored data. Computational Statistics, 25: 203–313. [Crossref], [Web of Science ®] , [Google Scholar]). The third estimator is the generalization of the Prentice and Cai (1992 Prentice, R. L. and Cai, J. 1992. Covariance and survivor function estimation using censored multivariate failure time data. Biometrika, 79: 495–512. [Crossref], [Web of Science ®] , [Google Scholar]) estimator. The consistency of the proposed M-estimators is established. A simulation study is conducted to investigate the performance of the proposed estimators. Furthermore, the simple bootstrap methods are used to estimate standard deviations and construct interval estimators.     

The Identification of Potential Longitudinal Biomarkers and Measurements of Effectiveness for Biomarkers as Surrogates in Multivariate Survival Data

A proposed method based on frailty models is used to identify longitudinal biomarkers or surrogates for a multivariate survival. This method is an extention of earlier models by Wulfsohn and Tsiatis (1997 Wulfsohn , M. S. , Tsiatis , A. A. ( 1997 ). A joint model for survival and longitudinal data measured with error . Biometrics 53 ( 1 ): 330 – 339 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) and Song et al. (2002 Song , X. , Davidian , M. , Tsiatis , A. A. ( 2002 ). A Semiparametric likelihood approach to joint modeling of longitudinal and time-to-event data . Biometrics 58 ( 4 ): 742 – 753 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). In this article, similar to Henderson et al. (2002 Henderson , R. , Diggle , P. J. , Dobson , A. ( 2002 ). Identification and efficacy of longitudinal markers for survival . Biostatistics 3 ( 1 ): 33 – 50 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), a joint likelihood function combines the likelihood functions of the longitudinal biomarkers and the multivariate survival times. We use simulations to explore how the number of individuals, the number of time points per individual and the functional form of the random effects from the longitudianl biomarkers influence the power to detect the association of a longitudinal biomarker and the multivariate survival time. The proposed method is illustrate by using the gastric cancer data.     

On the Feasibility of Basing Horvitz and Thompson's Estimator on a Sample by Rao,Hartley, and Cochran's Scheme

Formulae for the first and second order inclusion probabilities for the Rao et al. (1962 Rao , J. N. K. , Hartley , H. O. , Cochran , W. G. ( 1962 ). On a simple procedure of unequal probability sampling without replacement . J. Roy. Statist. Soc. B 24 : 482 – 491 . [CSA]  [Google Scholar]) (RHC) scheme of sampling are derived. They enable one to evaluate, for a sample drawn according to the RHC scheme, the Horvitz and Thompson's (1952 Horvitz , D. G. , Thompson , D. J. ( 1952 ). A generalization of sampling without replacement from a finite universe . J. Amer. Statist. Assoc. 47 : 663 – 685 . [CSA] [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) estimator (HTE) along with its unbiased variance estimator given by Yates and Grundy (1953 Yates , F. , Grundy , P. M. ( 1953 ). Selection without replacement from within strata with probability proportional to size . J. Amer. Statist. Assoc. 75 : 206 – 211 . [CSA]  [Google Scholar]). So, for a sample at hand thus drawn one may choose between the RHCE and the HTE for use on finding which one has the smaller coefficient of variation.     

On Complete Convergence for Arrays of Dependent Random Variables

A complete convergence theorem for an array of rowwise independent random variables was established by Sung et al. (2005 Sung , S. H. , Volodin , A. I. , Hu , T.-C. ( 2005 ). More on complete convergence for arrays . Statist. Probab. Lett. 71 : 303 – 311 .[Crossref], [Web of Science ®] , [Google Scholar]). This result has been generalized and extended by Kruglov et al. (2006 Kruglov , V. M. , Volodin , A. I. , Hu , T.-C. ( 2006 ). On complete convergence for arrays . Statist. Probab. Lett. 76 : 1631 – 1640 .[Crossref], [Web of Science ®] , [Google Scholar]) and Chen et al. (2007 Chen , P. , Hu , T.-C. , Liu , X. , Volodin , A. ( 2007 ). On complete convergence for arrays of rowwise negatively associated random variables . Theor. Probab. Appl. 52 : 393 – 397 . [Google Scholar]). In this article, we extend the results of Sung et al. (2005 Sung , S. H. , Volodin , A. I. , Hu , T.-C. ( 2005 ). More on complete convergence for arrays . Statist. Probab. Lett. 71 : 303 – 311 .[Crossref], [Web of Science ®] , [Google Scholar]), Kruglov et al. (2006 Kruglov , V. M. , Volodin , A. I. , Hu , T.-C. ( 2006 ). On complete convergence for arrays . Statist. Probab. Lett. 76 : 1631 – 1640 .[Crossref], [Web of Science ®] , [Google Scholar]), and Chen et al. (2007 Chen , P. , Hu , T.-C. , Liu , X. , Volodin , A. ( 2007 ). On complete convergence for arrays of rowwise negatively associated random variables . Theor. Probab. Appl. 52 : 393 – 397 . [Google Scholar]) to an array of dependent random variables satisfying Hoffmann-Jørgensen type inequalities.     

Estimating Incidence Rate on Current Status Data with Application to a Phase IV Cancer Trial

New drug discovery in the pediatrics has dramatically improved survival, but with long- term adverse events. This motivates the examination of adverse outcomes such as long-term toxicity in a phase IV trial. An ideal approach to monitor long-term toxicity is to systematically follow the survivors, which is generally not feasible. Instead, cross-sectional surveys are conducted in Hudson et al. (2007 Hudson , M. M. , Rai , S. N. , Nunez , C. , Merchant , T. E. , Marina , N. M. , Zalamea , N. , Cox , C. , Phipps , S. , Pompeu , R. , Rosenthal , D. ( 2007 ). Noninvasive evaluation of late anthracycline cardiac toxicity in childhood cancer survivors . J. Clin. Oncol. 25 : 3635 – 3643 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), with one of the objectives to estimate the cumulative incidence rates along with specific interest in fixed-term (5 or 10 year) rates. We present inference procedures based on current status data to our motivating example with very interesting findings.     

Analyzing Supersaturated Designs by Means of an Information Based Criterion

The cost and time consumption of many industrial experimentations can be reduced using the class of supersaturated designs since this can be used for screening out the important factors from a large set of potentially active variables. A supersaturated design is a design for which there are fewer runs than effects to be estimated. Although there exists a wide study of construction methods for supersaturated designs, their analysis methods are yet in an early research stage. In this article, we propose a method for analyzing data using a correlation-based measure, named as symmetrical uncertainty. This method combines measures from the information theory field and is used as the main idea of variable selection algorithms developed in data mining. In this work, the symmetrical uncertainty is used from another viewpoint in order to determine more directly the important factors. The specific method enables us to use supersaturated designs for analyzing data of generalized linear models for a Bernoulli response. We evaluate our method by using some of the existing supersaturated designs, obtained according to methods proposed by Tang and Wu (1997 Tang , B. , Wu , C. F. J. (1997). A method for constructing supersaturated designs and its E(s ²)-optimality. Canadian Journal of Statistics 25:191–201.[Crossref], [Web of Science ®] , [Google Scholar]) as well as by Koukouvinos et al. (2008 Koukouvinos , C. , Mylona , K. , Simos , D. E. ( 2008 ). E(s ²)-optimal and minimax-optimal cyclic supersaturated designs via multi-objective simulated annealing . Journal of Statistical Planning and Inference 138 : 1639 – 1646 .[Crossref], [Web of Science ®] , [Google Scholar]). The comparison is performed by some simulating experiments and the Type I and Type II error rates are calculated. Additionally, Receiver Operating Characteristics (ROC) curves methodology is applied as an additional statistical tool for performance evaluation.     

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.     

Bayesian Capture-Recapture Analysis: An Application in Modeling Semelparity of a Neotropical Didelphid Marsupial

We develop a series of Bayesian statistical models for estimating survival of a neotropic didelphid marsupial, the Brazilian gracile mouse opossum (Gracilinanus microtarsus). These models are based on the Cormack–Jolly–Seber model (Cormack, 1964 Cormack , R. M. ( 1964 ). Estimates of survival from the sighting of marked animals . Biometrika 51 : 429 – 438 .[Crossref], [Web of Science ®] , [Google Scholar]; Jolly 1965 Jolly , G. M. ( 1965 ). Explicit estimates from capture-recapture data with both death and immigration stochastic model . Biometrika 52 : 225 – 247 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Seber 1965 Seber , G. A. F. ( 1965 ). A note on the multiple recapture census . Biometrika 52 : 249 – 259 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) with both survival and recapture rates expressed as a function of covariates using a logit link. The proposed models allow taking into account heterogeneity in capture probability caused by the existence of different groups of individuals in the population. The models were applied to two cohorts (Cohort, 2000, 2001) with the first one including 14 and the second one 15 sampling occasions. The best models for each of the cohorts indicate that G. microtarsus is best described as partially semelparous, a condition in which mortality after the first mating is high but graded over time, with a fraction of males surviving for a second breeding season (Boonstra, 2005 Boonstra , R. ( 2005 ). Equipped for life: the adaptive role of the stress axis in male mammals . Journal of Mammalogy 86 : 236 – 247 .[Crossref], [Web of Science ®] , [Google Scholar]).     

Aspects of Dependence in Generalized Farlie-Gumbel-Morgenstern Distributions

In this article, we obtained a dependence measure for generalized Farlie-Gumbel-Morgenstern (FGM) family in view of Kochar and Gupta (1987 Kochar , S. G. , Gupta , R. P. ( 1987 ). Competitors of Kendall-tau test for testing independence against PQD . Biometrika 74 ( 3 ): 664 – 669 .[Crossref], [Web of Science ®] , [Google Scholar]) and then compared this measure with Spearman's rho and Kendall's tau in FGM family. Moreover, we evaluated the empirical power of 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 PQD . Biometrika 74 ( 3 ): 664 – 669 .[Crossref], [Web of Science ®] , [Google Scholar], 1990 Kochar , S. G. , Gupta , R. P. ( 1990 ). Distribution-free tests based on sub-sample extrema for testing against positive dependence . Australian Journal of Statistics 32 : 45 – 51 .[Crossref] , [Google Scholar]) based on exact distribution of a U-statistics. This is derived via a simulation study for sample of sizes n = 6, 8, 10, 12, 16, and 20. Also, we compared our simulation results with those achieved by Amini et al. (2010 Amini , M. , Jabbari , H. , Mohtashami Borzadaran , G. R. , Azadbakhsh , M. ( 2010 ). Power comparison of independence test for the Farlie-Gumbel-Moregenstern family . Communications of the Korean Statistical Society 17 ( 4 ): 493 – 505 .[Crossref] , [Google Scholar]) and Güven and Kotz (2008 Güven , B. , Kotz , S. ( 2008 ). Test of independence for generalized Farlie-Gumbel-Morgenstern distributions . Journal of Computational and Applied Mathematics 212 : 102 – 111 .[Crossref], [Web of Science ®] , [Google Scholar]).     

Improved Bar-Lev,Bobovitch, and Boukai Randomized Response Models

In this article, two new improved randomized response models have been proposed. The proposed models are found to be more efficient than the recent randomized response model studied by Bar-Lev et al. (2004 Bar-Lev , S. K. , Bobovitch , E. , Boukai , B. ( 2004 ). A note on randomized response models for quantitative data . Metrika 60 : 255 – 260 .[Crossref], [Web of Science ®] , [Google Scholar]). The relative efficiency of the proposed models has been studied with respect to the Bar-Lev et al. (2004 Bar-Lev , S. K. , Bobovitch , E. , Boukai , B. ( 2004 ). A note on randomized response models for quantitative data . Metrika 60 : 255 – 260 .[Crossref], [Web of Science ®] , [Google Scholar]) model under different situations.     

An Asymmetric Kernel Estimator of Density Function for Stationary Associated Sequences

Here, we apply the smoothing technique proposed by Chaubey et al. (2007 Chaubey , Y. P. , Sen , A. , Sen , P. K. ( 2007 ). A new smooth density estimator for non-negative random variables. Technical Report No. 1/07. Department of Mathematics and Statistics, Concordia University, Montreal, Canada . [Google Scholar]) for the empirical survival function studied in Bagai and Prakasa Rao (1991 Bagai , I. , Prakasa Rao , B. L. S. ( 1991 ). Estimation of the survival function for stationary associated processes . Statist. Probab. Lett. 12 : 385 – 391 .[Crossref], [Web of Science ®] , [Google Scholar]) for a sequence of stationary non-negative associated random variables.The derivative of this estimator in turn is used to propose a nonparametric density estimator. The asymptotic properties of the resulting estimators are studied and contrasted with some other competing estimators. A simulation study is carried out comparing the recent estimator based on the Poisson weights (Chaubey et al., 2011 Chaubey , Y. P. , Dewan , I. , Li , J. ( 2011 ). Smooth estimation of survival and density functions for a stationary associated process using poisson weights . Statist. Probab. Lett. 81 : 267 – 276 .[Crossref], [Web of Science ®] , [Google Scholar]) showing that the two estimators have comparable finite sample global as well as local behavior.     

Improved strategy to collect sensitive data by using geometric distribution as a randomization device

Abstract

In this article, we improvise Singh and Grewal (2013 Singh, S., and I. S. Grewal. 2013. Geometric distribution as a randomization device implemented in the Kuk’s model. International Journal of Contemporary Mathematical Sciences 8:243–8.[Crossref] , [Google Scholar]) and Hussain et al. (2016 Hussain, Z., J. Shabbir, Z. Pervez, S. F. Shah, and M. Khan. 2016. Generalized geometric distribution of order k: A flexible choice to randomize the response. Communications in Statistics: Simulation and Computation 46:4708–21.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) techniques by introducing a new two-stage randomization response process. Using the proposed new technique, we achieve better efficiency and increasing protection of privacy of respondents than the Kuk (1990 Kuk, A. Y. C. 1990. Asking sensitive questions indirectly. Biometrika 77 (2):436–8.[Crossref], [Web of Science ®] , [Google Scholar]), Singh and Grewal (2013 Singh, S., and I. S. Grewal. 2013. Geometric distribution as a randomization device implemented in the Kuk’s model. International Journal of Contemporary Mathematical Sciences 8:243–8.[Crossref] , [Google Scholar]) and Hussain et al. (2016 Hussain, Z., J. Shabbir, Z. Pervez, S. F. Shah, and M. Khan. 2016. Generalized geometric distribution of order k: A flexible choice to randomize the response. Communications in Statistics: Simulation and Computation 46:4708–21.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) models. The relative efficiency and protection of the respondents of the proposed two-stage randomization device have been investigated through simulation study, and the situations are reported where the proposed estimator performs better than its competitors. The SAS code used to investigate the performance of the proposed strategy are also provided.     

Tests for Multiple Outliers in an Exponential Sample

By applying the recursion of Huffer (1988 Huffer, F. 1988. Divided differences and the joint distribution of linear combinations of spacings. Journal of Applied Probability, 25: 346–354. [Crossref], [Web of Science ®] , [Google Scholar]) repeatedly, we propose an algorithm for evaluating the null joint distribution of Dixon-type test statistics for testing discordancy of k upper outliers in exponential samples. By using the critical values of Dixon-type test statistics determined from the proposed algorithm and those of Cochran-type test statistics presented earlier by Lin and Balakrishnan (2009 Lin, C. T. and Balakrishnan, N. 2009. Exact computation of the null distribution of a test for multiple outliers in an exponential sample. Computational Statistics & Data Analysis, 53: 3281–3290. [Crossref], [Web of Science ®] , [Google Scholar]), we carry out an extensive Monte Carlo study to investigate the powers and the error probabilities for the effects of masking and swamping when the number of outliers k = 2 and 3. Based on our empirical findings, we recommend Rosner’s (1975 Rosner, B. 1975. On the detection of many outliers. Technometrics, 17: 221–227. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) sequential test procedure based on Dixon-type test statistics for testing multiple outliers from an exponential distribution.     

Using Frailty Models to Identify the Longitudinal Biomarkers in Survival Analysis

We introduce a score test to identify longitudinal biomarkers or surrogates for a time to event outcome. This method is an extension of Henderson et al. (2000 Henderson , R. , Diggle , P. , Dobson , A. ( 2000 ). Joint modelling of longitudinal measurements and event time data . Biostatistics 1 ( 4 ): 465 – 480 .[Crossref], [PubMed] , [Google Scholar], 2002 Henderson , R. , Diggle , P. , Dobson , A. ( 2002 ). Identification and efficacy of longitudinal markers for survival . Biostatistics 3 ( 1 ): 33 – 50 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). In this article, a score test is based on a joint likelihood function which combines the likelihood functions of the longitudinal biomarkers and the survival times. Henderson et al. (2000 Henderson , R. , Diggle , P. , Dobson , A. ( 2000 ). Joint modelling of longitudinal measurements and event time data . Biostatistics 1 ( 4 ): 465 – 480 .[Crossref], [PubMed] , [Google Scholar], 2002 Henderson , R. , Diggle , P. , Dobson , A. ( 2002 ). Identification and efficacy of longitudinal markers for survival . Biostatistics 3 ( 1 ): 33 – 50 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) assumed that the same random effect exists in the longitudinal component and in the Cox model and then they can derive a score test to determine if a longitudinal biomarker is associated with time to an event. We extend this work and our score test is based on a joint likelihood function which allows other random effects to be present in the survival function.

Considering heterogeneous baseline hazards in individuals, we use simulations to explore how the factors can influence the power of a score test to detect the association of a longitudinal biomarker and the survival time. These factors include the functional form of the random effects from the longitudinal biomarkers, in the different number of individuals, and time points per individual. We illustrate our method using a prothrombin index as a predictor of survival in liver cirrhosis patients.     

The Finite Time Ruin Probability of a New Risk Model Based on Entrance Process

In this article, we consider a new insurance risk model based on the entrance process proposed in Li et al. (2005 Li , Z. , Zhu , J. , Chen , F. ( 2005 ). Study of a risk model based on the entrance process . Statist. Probab. Lett. 72 : 1 – 10 .[Crossref], [Web of Science ®] , [Google Scholar]), and investigate the finite time ruin probabilities of this model. It is showed that an exponential upper bound for the finite time ruin probability exists, when the distributions of the claim size are light tailed. Furthermore, when the distributions of the claim size are heavy tailed, an asymptotic formula for the finite time ruin probability is obtained.     

Data-Driven Tests for Trend

This article proposes a new nonparametric test for the ordered alternatives problem in the k-sample setting for null hypothesis of lack of trend. This article further elaborates upon and extends the results of Ledwina and Wy?upek (2012a Ledwina , T. , Wy?upek , G. ( 2012a ). Two-sample test against one-sided alternatives . Scand. J. Statist. 39 : 358 – 381 .[Crossref], [Web of Science ®] , [Google Scholar]) obtained for k = 2. Simulations show that the new test has high and stable power and is able to control the Type I error to satisfactory extent, thus solving the problem posed in Terpstra and Magel (2003 Terpstra , J. T. , Magel , R. C. ( 2003 ). A new nonparametric test for the ordered alternative problem . J. Nonparametr. Statist. 15 : 289 – 301 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). Our theoretical results say that asymptotic errors of both kinds do not exceed significance level, thus implying that the test is asymptotically unbiased.     

A Generalization of the Skew-Normal Distribution: The Beta Skew-Normal

We consider a new generalization of the skew-normal distribution introduced by Azzalini (1985 Azzalini , A. ( 1985 ). A class of distributions which includes the normal ones . Scand. J. Statis. 12 ( 2 ): 171 – 178 .[Web of Science ®] , [Google Scholar]). We denote this distribution Beta skew-normal (BSN) since it is a special case of the Beta generated distribution (Jones, 2004 Jones , M. C. ( 2004 ). Families of distributions of order statistics . Test 13 ( 1 ): 1 – 43 .[Crossref], [Web of Science ®] , [Google Scholar]). Some properties of the BSN are studied. We pay attention to some generalizations of the skew-normal distribution (Bahrami et al., 2009 Bahrami , W. , Agahi , H. , Rangin , H. ( 2009 ). A two-parameter Balakrishnan skew-normal distribution . J. Statist. Res. Iran 6 : 231 – 242 . [Google Scholar]; Sharafi and Behboodian, 2008 Sharafi , M. , Behboodian , J. ( 2008 ). The Balakrishnan skew-normal density . Statist. Pap. 49 : 769 – 778 .[Crossref], [Web of Science ®] , [Google Scholar]; Yadegari et al., 2008 Yadegari , I. , Gerami , A. , Khaledi , M. J. ( 2008 ). A generalization of the Balakrishnan skew-normal distribution . Statist. Probab. Lett. 78 : 1165 – 1167 .[Crossref], [Web of Science ®] , [Google Scholar]) and to their relations with the BSN.