Group Variable Selection with Oracle Property by Weight-Fused Adaptive Elastic Net Model for Strongly Correlated Data

This paper is the generalization of weight-fused elastic net (Fu and Xu, 2012 Fu, G., Xu, Q. (2012). Grouping variable selection by weight fused elastic net for multi-collinear data. Communications in Statistics-Simulation and Computation 41(2):205–221.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), which performs group variable selection by combining weight-fused LASSO(wfLasso) and elastic net (Zou and Hastie, 2005 Zou, H., Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 67(2):301–320.[Crossref], [Web of Science ®] , [Google Scholar]) penalties. In this study, the elastic net penalty is replaced by adaptive elastic net penalty (AdaEnet) (Zou and Zhang, 2009 Zou, H., Zhang, H. (2009). On the adaptive elastic-net with a diverging number of parameters. Annals of Statistics 37(4):1733–1751.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), and a new group variable selection algorithm with oracle property (Fan and Li, 2001 Fan, J., Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 96(456):1348–1360.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Zou, 2006 Zou, H. (2006). The adaptive lasso and its oracle properties. Journal of the American Statistical Association 101(476):1418–1429.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) is obtained.     

On Fitting Transformation Model to Survey Data

In this article, we consider fitting a semiparametric linear model to survey data with censored observations. The specific goal of the paper is to extend the methods of Cheng et al. (1995 Cheng, S.C., Wei, L.J., Ying, Z. (1995). Analysis of transformation models with censored data. Biometrika 82(4):835–845.[Crossref], [Web of Science ®] , [Google Scholar]) and Chen et al. (2002 Chen, K., Jin, Z. Ying, Z. (2002). Semiparametric analysis of transformation models with censored data. Biometrika 89:659–668.[Crossref], [Web of Science ®] , [Google Scholar]) to the case when the sample has been drawn from a population using a complex sampling design. Similar to the approach of Lin (2000 Lin, D.Y. (2000). On fitting Cox’s proportional hazards models to survey data. Biometrika 87:37–47.[Crossref], [Web of Science ®] , [Google Scholar]), we regard the survey population as a random sample from an infinite universe and accounts for this randomness in the statistical inference. A simulation study is conducted to investigate the performance of the proposed estimators.     

An adaptive multivariate CUSUM control chart for signaling a range of location shifts

ABSTRACT

In this work, we proposed an adaptive multivariate cumulative sum (CUSUM) statistical process control chart for signaling a range of location shifts. This method was based on the multivariate CUSUM control chart proposed by Pignatiello and Runger (1990 Pignatiello, J.J., Runger, G.C. (1990). Comparisons of multivariate CUSUM charts. J. Qual. Technol. 22(3):173–186.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), but we adopted the adaptive approach similar to that discussed by Dai et al. (2011 Dai, Y., Luo, Y., Li, Z., Wang, Z. (2011). A new adaptive CUSUM control chart for detecting the multivariate process mean. Qual. Reliab. Eng. Int. 27(7):877–884.[Crossref], [Web of Science ®] , [Google Scholar]), which was based on a different CUSUM method introduced by Crosier (1988 Crosier, R.B. (1988). Multivariate generalizations of cumulative sum quality-control schemes. Technometrics 30(3):291–303.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The reference value in this proposed procedure was changed adaptively in each run, with the current mean shift estimated by exponentially weighted moving average (EWMA) statistic. By specifying the minimal magnitude of the mean shift, our proposed control chart achieved a good overall performance for detecting a range of shifts rather than a single value. We compared our adaptive multivariate CUSUM method with that of Dai et al. (2001 Dai, Y., Luo, Y., Li, Z., Wang, Z. (2011). A new adaptive CUSUM control chart for detecting the multivariate process mean. Qual. Reliab. Eng. Int. 27(7):877–884.[Crossref], [Web of Science ®] , [Google Scholar]) and the non adaptive versions of these two methods, by evaluating both the steady state and zero state average run length (ARL) values. The detection efficiency of our method showed improvements over the comparative methods when the location shift is unknown but falls within an expected range.     

Generalized linear regression models incorporating original outcome distributions

ABSTRACT

In this article, we propose an approach for incorporating continuous and discrete original outcome distributions into the usual exponential family regression models. The new approach is an extension of the works of Suissa (1991 Suissa, S. (1991). Binary methods for continuous outcomes: A parametric alternative. J. Clin. Epidemiol. 44:241–248.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) and Suissa and Blais (1995 Suissa, S., Blais, L. (1995). Binary regression with continuous outcomes. Stat. Med. 14:247–255.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), which present methods to estimate the risk of an event defined in a sample subspace of an original continuous outcome variable. Simulation studies are presented in order to illustrate the performance of the developed methodology. Real data sets are analyzed by using the proposed models.     

Note on posterior inference for the Bingham distribution

The properties of high-dimensional Bingham distributions have been studied by Kume and Walker (2014 Kume, A., and S. G. Walker. 2014. On the Bingham distribution with large dimension. Journal of Multivariate Analysis 124:345–52.[Crossref], [Web of Science ®] , [Google Scholar]). Fallaize and Kypraios (2016 Fallaize, C. J., and T. Kypraios. 2016. Exact Bayesian inference for the Bingham distribution. Statistics and Computing 26:349–60.[Crossref], [Web of Science ®] , [Google Scholar]) propose the Bayesian inference for the Bingham distribution and they use developments in Bayesian computation for distributions with doubly intractable normalizing constants (Møller et al. 2006 Møller, J., A. N. Pettitt, R. Reeves, and K. K. Berthelsen. 2006. An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants. Biometrika 93 (2):451–458.[Crossref], [Web of Science ®] , [Google Scholar]; Murray, Ghahramani, and MacKay 2006 Murray, I., Z. Ghahramani, and D. J. C. MacKay. 2006. MCMC for doubly intractable distributions. In Proceedings of the 22nd annual conference on uncertainty in artificial intelligence (UAI-06), 359–66. AUAI Press. [Google Scholar]). However, they rely heavily on two Metropolis updates that they need to tune. In this article, we propose instead a model selection with the marginal likelihood.     

Equivalent Conditions of Complete Moment Convergence of Weighted Sums for ϕ-Mixing Sequence of Random Variables

In this article, the complete moment convergence of weighted sums for ?-mixing sequence of random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete moment convergence of weighted sums for ?-mixing sequence of random variables are established. These results promote and improve the corresponding results obtained by Li et al. (1995 Li, D.L., Rao, M.B., Jiang, T.F., Wang, X.C. (1995). Complete convergence and almost sure convergence of weighted sums of random variables. J. Theoret. Probab. 8:49–76.[Crossref], [Web of Science ®] , [Google Scholar]) and Gut (1993 Gut, A. (1993). Complete convergence and Cesàro summation for i.i.d. random variables. Probab. Theory Related Fields 97:169–178.[Crossref], [Web of Science ®] , [Google Scholar]) from i.i.d. to ?-mixing setting. Moreover, we obtain the complete moment convergence of moving average processes based on ?-mixing random variables, which extends the result of Kim et al. (2008 Kim, T.S., Ko, M.H. (2008). Complete moment convergence of moving average processes under dependence assumptions. Statist. Probab. Lett. 78:839–846.[Crossref], [Web of Science ®] , [Google Scholar]) in the sense that it does not require a specific mixing rate.     

A new lifetime model with different types of failure rate

A new class of lifetime distributions, which can exhibit with upside-down bathtub-shaped, bathtub-shaped, decreasing, and increasing failure rates, is introduced. The new distribution is constructed by compounding generalized Weibull and logarithmic distributions, leading to improvement on the lifetime distribution considered in Dimitrakopoulou et al. (2007 Dimitrakopoulou, T., K. Adamidis, and S. Loukas. 2007. A lifetime distribution with an upside-down bathtub-shaped hazard function. IEEE Transactions on Reliability 56:308–11.[Crossref], [Web of Science ®] , [Google Scholar]) by having no restriction on the shape parameter and extending the result studied by Tahmasbi and Rezaei (2008 Tahmasbi, R., and S. Rezaei. 2008. A two-parameter lifetime distribution with decreasing failure rate. Computational Statistics and Data Analysis 52:3889–901.[Crossref], [Web of Science ®] , [Google Scholar]) in the general form. The proposed model includes the exponential–logarithmic and Weibull–logarithmic distributions as special cases. Various statistical properties of the proposed class are discussed. Furthermore, estimation via the maximum likelihood method and the Fisher information matrix are discussed. Applications to real data demonstrate that the new class of distributions is more flexible than other recently proposed classes.     

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.     

On Augmented Franses Tests for Seasonal Unit Roots

This article extends the results reported in del Barrio Castro, Osborn and Taylor (2012 del Barrio Castro, T., Osborn, D.R., Taylor, A. M.R. (2012). On augmented HEGY tests for seasonal unit roots. Econometric Theor. 18:1121–1143.[Crossref], [Web of Science ®] , [Google Scholar]) to the approach followed by Franses (1991a Franses, P. H. (1991a). Model selection and seasonality in time series. Tibergen Institute Series, 18. [Google Scholar],b Franses, P.H. (1991b). Seasonality, non-stationarity and the forecasting of monthly time series. Int. J. Forecast. 7:199–208.[Crossref], [Web of Science ®] , [Google Scholar]) to test for seasonal unit roots, providing the asymptotic representation to the seasonal unit roots tests proposed by Franses for a general number of seasons S.     

Baker- Lin-Huang Type Bivariate Distributions Based on Order Statistics

Baker (2008 Baker, R. (2008). An order-statistics-based method for constructing multivariate distributions with fixed marginals. J. Multivariate Anal. 99: 23122327.[Crossref], [Web of Science ®] , [Google Scholar]) introduced a new class of bivariate distributions based on distributions of order statistics from two independent samples of size n. Lin and Huang (2010 Lin, G.D., Huang, J.S. (2010). A note on the maximum correlation for Baker’s bivariate distributions with fixed marginals. J. Multivariate Anal. 101: 22272233.[Crossref], [Web of Science ®] , [Google Scholar]) discovered an important property of Baker’s distribution and showed that the Pearson’s correlation coefficient for this distribution converges to maximum attainable value, i.e., the correlation coefficient of the Fréchet upper bound, as n increases to infinity. Bairamov and Bayramoglu (2013 Bairamov, I., Bayramoglu, K. (2013). From Huang-Kotz distribution to Baker’s distribution. J. Multivariate Anal. 113: 106115.[Crossref], [Web of Science ®] , [Google Scholar]) investigated a new class of bivariate distributions constructed by using Baker’s model and distributions of order statistics from dependent random variables, allowing higher correlation than that of Baker’s distribution. In this article, a new class of Baker’s type bivariate distributions with high correlation are constructed based on distributions of order statistics by using an arbitrary continuous copula instead of the product copula.     

Heavy traffic analysis of roving server networks

This article studies the heavy-traffic (HT) behavior of queueing networks with a single roving server. External customers arrive at the queues according to independent renewal processes and after completing service, a customer either leaves the system or is routed to another queue. This type of customer routing in queueing networks arises very naturally in many application areas (in production systems, computer- and communication networks, maintenance, etc.). In these networks, the single most important characteristic of the system performance is oftentimes the path time, i.e., the total time spent in the system by an arbitrary customer traversing a specific path. The current article presents the first HT asymptotic for the path-time distribution in queueing networks with a roving server under general renewal arrivals. In particular, we provide a strong conjecture for the system’s behavior under HT extending the conjecture of Coffman et al.^{[8 Coffman, Jr, E. G.; Puhalskii, A. A.; Reiman, M. I,. Polling systems with zero switchover times: A heavy-traffic averaging principle. Ann. App. Prob. 1995, 5(3), 681–719.[Crossref], [Web of Science ®] [Google Scholar],9 Coffman, Jr., E. G.; Puhalskii, A. A.; Reiman, M. I,. Polling systems in heavy-traffic: A Bessel process limit. Math. Oper. Res. 1998, 23, 257–304.[Crossref], [Web of Science ®] [Google Scholar]]} to the roving server setting of the current article. By combining this result with novel light-traffic asymptotics, we derive an approximation of the mean path time for arbitrary values of the load and renewal arrivals. This approximation is not only highly accurate for a wide range of parameter settings, but is also exact in various limiting cases.     

A quantile-based study on ageing intensity function

Jiang, Ji, and Xiao (2003 Jiang, R., P. Ji, and X. Xiao. 2003. Aging property of unimodal failure rate models. Reliability Engineering and System Safety 79(1):113–6.[Crossref], [Web of Science ®] , [Google Scholar]) has introduced a quantitative measure known as the ageing intensity function for evaluating the ageing properties of a component/system. In recent years, there has been a great interest on the study of quantile function, an equivalent alternative to the distribution function approach. Unlike the distribution function approach, the quantile method possess some unique properties (see Gilchrist 2000 Gilchrist, W. 2000. Statistical modelling with quantile functions. Boca Raton, Florida: Chapman and Hall/CRC.[Crossref] , [Google Scholar], Nair, Sankaran, and Balakrishnan 2013 Nair N. U., P. G. Sankaran, N. Balakrishnan. 2013. Quantile-based reliability concepts. In: Quantile-Based Reliability Analysis. Statistics for Industry and Technology. New York, NY: Birkhäuser.[Crossref] , [Google Scholar]). Motivated with this, in the present paper we introduce a quantile-based ageing intensity function and study its various ageing properties. We also study some stochastic comparison of random variables based on the proposed measure.     

Inference in log-alpha-power and log-skew-normal multivariate models

ABSTRACT

Random vectors with positive components are common in many applied fields, for example, in meteorology, when daily precipitation is measured through a region Marchenko and Genton (2010 Marchenko, Y., Genton, M. (2010). Multivariate log-skew-elliptical distributions with applications to precipitation data. Environmetrics 21:318–340.[Crossref], [Web of Science ®] , [Google Scholar]). Frequently, the log-normal multivariate distribution is used for modeling this type of data. This modeling approach is not appropriate for data with high asymmetry or kurtosis. Consequently, more flexible multivariate distributions than the log-normal multivariate are required. As an alternative to this distribution, we propose the log-alpha-power multivariate and log-skew-normal multivariate models. The first model is an extension for positive data of the fractional order statistics model Durrans (1992 Durrans, S. (1992). Distributions of fractional order statistics in hydrology. Water Resour. Res. 28:1649–1655.[Crossref], [Web of Science ®] , [Google Scholar]). The second one is an extension of the log-skew-normal model studied by Mateu-Figueras and Pawlowsky-Glahn (2007 Mateu-Figueras, G., Pawlowsky-Glahn, V. (2007). The skew-normal distribution on the simplex. Commun. Stat.-Theory Methods 36:1787–1802.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). We study parameter estimation for these models by means of pseudo-likelihood and maximum likelihood methods. We illustrate the proposal analyzing a real dataset.     

On goodness-of-fit tests for Aalen's additive model based on left-truncated right-censored or doubly censored data

ABSTRACT

Gandy and Jensen (2005 Gandy, A., Jensen, U. (2005). On goodness-of-fit tests for Aalen's additive risk model. Scan. J. Stat. 32:425–445.[Crossref], [Web of Science ®] , [Google Scholar]) proposed goodness-of-fit tests for Aalen's additive risk model. In this article, we demonstrate that the approach of Gandy and Jensen (2005 Gandy, A., Jensen, U. (2005). On goodness-of-fit tests for Aalen's additive risk model. Scan. J. Stat. 32:425–445.[Crossref], [Web of Science ®] , [Google Scholar]) can be applied to left-truncated right-censored (LTRC) data and doubly censored data. A simulation study is conducted to investigate the performance of the proposed tests. The proposed tests are illustrated using heart transplant data.     

Bayes minimax ridge regression estimators

The problem of estimating of the vector β of the linear regression model y = Aβ + ? with ? ～ N_p(0, σ²I_p) under quadratic loss function is considered when common variance σ² is unknown. We first find a class of minimax estimators for this problem which extends a class given by Maruyama and Strawderman (2005 Maruyama, Y., and W. E. Strawderman. 2005. A new class of generalized Bayes minimax ridge regression estimators. Annals of Statistics 33:1753–70.[Crossref], [Web of Science ®] , [Google Scholar]) and using these estimators, we obtain a large class of (proper and generalized) Bayes minimax estimators and show that the result of Maruyama and Strawderman (2005 Maruyama, Y., and W. E. Strawderman. 2005. A new class of generalized Bayes minimax ridge regression estimators. Annals of Statistics 33:1753–70.[Crossref], [Web of Science ®] , [Google Scholar]) is a special case of our result. We also show that under certain conditions, these generalized Bayes minimax estimators have greater numerical stability (i.e., smaller condition number) than the least-squares estimator.     

Quantile Regression with Left-Truncated and Right-Censored Data in a Reproducing Kernel Hilbert Space

Li et al. (2007 Li, Y., Liu, Y., Zhu, J. (2007). Quantile regression in reproducing kernel Hilbert spaces. J. Amer. Statist. Assoc. 102:255–268.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) developed an estimation method for quantile functions in a reproducing kernel Hilbert space for complete data, and Park and Kim (2011 Park, J., Kim, J. (2011). Quantile regression with an epsilon-insensitive loss in a reproducing kernel Hilbert space. Statist. Probab. Lett. 81:62–70.[Crossref], [Web of Science ®] , [Google Scholar]) proposed an estimation method using the ε-insensitive loss. This article extends these estimation methods to left-truncated and right-censored data. As a measure of goodness of fit, the check loss and the ε-insensitive loss were used to estimate the quantile function. The ε-insensitive loss can shrink the estimated coefficients toward zero; hence, it can reduce the variability of the estimates. Simulation studies show that the estimated quantile functions based on the ε-insensitive loss perform slightly better when ε is adequately chosen.     

A Strong Limit Theorem for Weighted Sums of Negatively Dependent Random Variables

In this article, we establish a new complete convergence theorem for weighted sums of negatively dependent random variables. As corollaries, many results on the almost sure convergence and complete convergence for weighted sums of negatively dependent random variables are obtained. In particular, the results of Jing and Liang (2008 Jing, B.Y., Liang, H.Y. (2008). Strong limit theorems for weighted sums of negatively associated random variables. J. Theor. Probab. 21:890–909.[Crossref], [Web of Science ®] , [Google Scholar]), Sung (2012 Sung, S.H. (2012). Complete convergence for weighted sums of negatively dependent random variables. Stat. Pap. 53:73–82.[Crossref], [Web of Science ®] , [Google Scholar]), and Wu (2010) can be obtained.     

On simulation of normal records

ABSTRACT

In the present paper, we discuss algorithms of record generation when records are taken from a normal population. We propose three new generation algorithms, compare their efficiency and find the most efficient algorithm (Algorithm 2.1). We then compare these algorithms with known generation algorithms presented in the work of Balakrishnan, So, and Zhu (2016 Balakrishnan, N., H. Y. So, and X. J. Zhu. 2016. On Box-Muller transformation and simulation of normal record data. Communication in Statistics – Simulation and Computations 45(10):3670–82.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]).     

On General Continuous Triangular and Two-sided Power Distributions

In this article, we directly introduce the continuous version of the general discrete triangular distributions (Kokonendji and Zocchi, 2010 Kokonendji, C.C., Zocchi, S.S. (2010). Extensions of discrete triangular distribution and boundary bias in kernel estimation for discrete functions. Statist. Probab. Lett. 80:1655–1662.[Crossref], [Web of Science ®] , [Google Scholar]). It is bounded and, in general, unimodal with pike. It contains thus a very useful class of two-sided power distributions (van Dorp and Kotz, 2002a Van Dorp, J.R., Kotz, S. (2002a). A novel extension of the triangular distribution and its parameter estimation. Statistician 51:1–17. [Google Scholar],b Van Dorp, J.R., Kotz, S. (2002b). The standard two-sided power distribution and its properties; with applications in financial engineering. Amer. Statistician 56:90–99.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar], 2003 Van Dorp, J.R., Kotz, S. (2003). Generalization of two-sided power distributions and their convolution. Commun. Statist. Theor. Meth. 32:1703–1723.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). Moments, particular cases, limit distributions, and relations between parameters are straightforwardly derived.     

Further Results for a General Family of Bivariate Copulas

A bivariate family of copulas has been initiated by Cuadras-Augé (1981 Cuadras, C.M., Augé, J. (1981). A continuous general multivariate distribution and its properties. Commun. Statist. (A) Theor. Meth. 10:339–353.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and Marshall (1996 Marshall, A.W. (1996). Copulas, marginals, and joint distributions. In: Distributions with fixed marginals and related topics. IMS Lecture Notes Monogr. Ser. 28:213–222.[Crossref] , [Google Scholar]). Recently, Durante (2007 Durante, F. (2007). A new family of symmetric bivariate copulas. C. R. Math. Acad. Sci. Paris 344:195–198.[Crossref], [Web of Science ®] , [Google Scholar]) considered this family as a general family of symmetric bivariate copulas indexed by a generator function and studied some of its dependence properties. In this article, we obtain and describe further aspects of dependence for this family. For example, we have proved that the family has positive likelihood ratio dependence structure if and only if the family reduces to some well-known copulas. We also derive several proper forms for the generator function of this family. Considering a multivariate extension of the bivariate family of copulas provided by Durante et al. (2007 Durante, F., Quesada-Molina, J.J., Flores, M. (2007). On a family of multivariate copulas for aggregation processes. Inform. Sci. 177(24):5715–5724.[Crossref], [Web of Science ®] , [Google Scholar]), some dependence properties are studied. Finally, some positive dependence stochastic orderings for two random vectors having a copula from the proposed families, are discussed.