Metrika [SJR: 0.605] [H-I: 30] [2 followers] Follow Hybrid journal (It can contain Open Access articles) ISSN (Print) 1435-926X - ISSN (Online) 0026-1335 Published by Springer-Verlag [2335 journals] |
- A new joint model of recurrent event data with the additive hazards model
for the terminal event time- Authors: Xiaoyu Che; John Angus
Pages: 763 - 787
Abstract: Abstract Recurrent event data are frequently encountered in clinical and observational studies related to biomedical science, econometrics, reliability and demography. In some situations, recurrent events serve as important indicators for evaluating disease progression, health deterioration, or insurance risk. In statistical literature, non informative censoring is typically assumed when statistical methods and theories are developed for analyzing recurrent event data. In many applications, however, there may exist a terminal event, such as death, that stops the follow-up, and it is the correlation of this terminal event with the recurrent event process that is of interest. This work considers joint modeling and analysis of recurrent event and terminal event data, with the focus primarily on determining how the terminal event process and the recurrent event process are correlated (i.e. does the frequency of the recurrent event influence the risk of the terminal event). We propose a joint model of the recurrent event process and the terminal event, linked through a common subject-specific latent variable, in which the proportional intensity model is used for modeling the recurrent event process and the additive hazards model is used for modeling the terminal event time.
PubDate: 2016-10-01
DOI: 10.1007/s00184-016-0577-9
Issue No: Vol. 79, No. 7 (2016)
- Authors: Xiaoyu Che; John Angus
- Statistical inference for critical continuous state and continuous time
branching processes with immigration- Authors: Mátyás Barczy; Kristóf Körmendi; Gyula Pap
Pages: 789 - 816
Abstract: Abstract We study asymptotic behavior of conditional least squares estimators for critical continuous state and continuous time branching processes with immigration based on discrete time (low frequency) observations.
PubDate: 2016-10-01
DOI: 10.1007/s00184-016-0578-8
Issue No: Vol. 79, No. 7 (2016)
- Authors: Mátyás Barczy; Kristóf Körmendi; Gyula Pap
- On the skewness of order statistics in multiple-outlier PHR models
- Authors: Ebrahim Amini-Seresht; Jianfei Qiao; Yiying Zhang; Peng Zhao
Pages: 817 - 836
Abstract: Abstract In this paper, we investigate the skewness of order statistics stemming from multiple-outlier proportional hazard rates samples in the sense of several variability orderings such as the star order, Lorenz order and dispersive order. It is shown that the more heterogeneity among the multiple-outlier components will lead to a more skewed lifetime of a k-out-of-n system consisting of these components. The results established here generalize the corresponding ones in Kochar and Xu (J Appl Probab 48:271–284, 2011, Ann Oper Res 212:127–138, 2014). Some numerical examples are also provided to illustrate the theoretical results.
PubDate: 2016-10-01
DOI: 10.1007/s00184-016-0579-7
Issue No: Vol. 79, No. 7 (2016)
- Authors: Ebrahim Amini-Seresht; Jianfei Qiao; Yiying Zhang; Peng Zhao
- Exceedances of records
- Authors: A. Castaño-Martínez; F. López-Blázquez; B. Salamanca-Miño
Pages: 837 - 866
Abstract: Abstract Given a sequence of random variables (rv’s) and a real function \(\psi \) , the \(\psi \) -exceedances form a subsequence consisting of those rv’s larger than a function, \(\psi \) , of the previous element of the subsequence. We present the basic distribution theory of \(\psi \) -exceedances for a sequence of independent and identically distributed rv’s. We give several examples and we study with more detail the case of exponential parents with \(\psi \) a linear function. The particular case of arithmetic exceedances is useful to describe the behavior of a type I counter when the arrival process of particles follows a non-homogeneous Poisson process. We also mention applications to destructive testing, early alert systems and the departure process of a \(M_t/D/1/1\) queue.
PubDate: 2016-10-01
DOI: 10.1007/s00184-016-0580-1
Issue No: Vol. 79, No. 7 (2016)
- Authors: A. Castaño-Martínez; F. López-Blázquez; B. Salamanca-Miño
- Quantile inference based on clustered data
- Authors: Omer Ozturk; Asuman Turkmen
Pages: 867 - 893
Abstract: Abstract One-sample sign test is one of the common procedures to develop distribution-free inference for a quantile of a population. A basic requirement of this test is that the observations in a sample must be independent. This assumption is violated in certain settings, such as clustered data, grouped data and longitudinal studies. Failure to account for dependence structure leads to erroneous statistical inferences. In this study, we have developed statistical inference for a population quantile of order p in either balanced or unbalanced designs by incorporating dependence structure when the distribution of within-cluster observations is exchangeable. We provide a point estimate, develop a testing procedure and construct confidence intervals for a population quantile of order p. Simulation studies are performed to demonstrate that the confidence intervals achieve their nominal coverage probabilities. We finally apply the proposed procedure to Academic Performance Index data.
PubDate: 2016-10-01
DOI: 10.1007/s00184-016-0581-0
Issue No: Vol. 79, No. 7 (2016)
- Authors: Omer Ozturk; Asuman Turkmen
- Evaluations of expectations of order statistics and spacings based on IFR
distributions- Authors: Agnieszka Goroncy; Tomasz Rychlik
Pages: 635 - 657
Abstract: Abstract We consider i.i.d. random variables \(X_1,\ldots , X_n\) with a distribution function F preceding the exponential distribution function V in the convex transform order which means that F has an increasing failure rate. We determine sharp upper bounds on the expectations of order statistics and spacings based on \(X_1,\ldots , X_n\) , expressed in the population standard deviation units. We also specify the distributions for which all these bounds are attained. Finally, we indicate some reliability applications.
PubDate: 2016-08-01
DOI: 10.1007/s00184-015-0570-8
Issue No: Vol. 79, No. 6 (2016)
- Authors: Agnieszka Goroncy; Tomasz Rychlik
- Variability ordering of multiplicative frailty models
- Authors: Hongmei Xie; Keshe Ni; Wenyu Liu
Pages: 659 - 670
Abstract: Abstract The classical multiplicative frailty model in survival analysis accounts for unobserved heterogeneity between individuals. It is of great importance to identify how the variation of the frailty variable affects that of the overall population. This paper is mainly to present how the dispersive and the excess wealth orders between two frailty variables, translate into the corresponding orders between the resulting overall population variables. For the mean residual life and the mean inactivity time orders, we also obtain relevant analogous results in multiplicative frailty models.
PubDate: 2016-08-01
DOI: 10.1007/s00184-015-0571-7
Issue No: Vol. 79, No. 6 (2016)
- Authors: Hongmei Xie; Keshe Ni; Wenyu Liu
- Robust Bayesian Pitman closeness
- Authors: Jafar Ahmadi; Elham Mirfarah; Ahmad Parsian
Pages: 671 - 691
Abstract: Abstract In this paper, the robust Bayesian methodology has been developed in the sense of Pitman measure of closeness. To do this, the definition of Pitman posterior closeness, introduced by Ghosh and Sen (Commun Stat Theory Methods 20:3659–3678, 1991) and simultaneous closeness are integrated. First, the \(\varGamma \) -minimax problem is developed in the sense of Pitman’s criterion and the basic results and definitions are provided. Then, several results regarding Pitman \(\varGamma \) -minimax have been proved. Some examples have been presented to illustrate the application of the findings. Finally, other aspect of robust Bayesian methodology such as: Pitman stable rules and Pitman regret type estimators have been proposed.
PubDate: 2016-08-01
DOI: 10.1007/s00184-015-0572-6
Issue No: Vol. 79, No. 6 (2016)
- Authors: Jafar Ahmadi; Elham Mirfarah; Ahmad Parsian
- Likelihood ratio order of parallel systems with heterogeneous Weibull
components- Authors: Longxiang Fang; N. Balakrishnan
Pages: 693 - 703
Abstract: Abstract In this paper, we compare the largest order statistics arising from independent heterogeneous Weibull random variables based on the likelihood ratio order. Let \(X_{1},\ldots ,X_{n}\) be independent Weibull random variables with \(X_{i}\) having shape parameter \(0<\alpha \le 1\) and scale parameter \(\lambda _{i}\) , \(i=1,\ldots ,n\) , and \(Y_{1},\ldots ,Y_{n}\) be a random sample of size n from a Weibull distribution with shape parameter \(0<\alpha \le 1\) and a common scale parameter \(\overline{\lambda }=\frac{1}{n}\sum \nolimits _{i=1}^{n}\lambda _{i}\) , the arithmetic mean of \(\lambda _{i}^{'}s\) . Let \(X_{n:n}\) and \(Y_{n:n}\) denote the corresponding largest order statistics, respectively. We then prove that \(X_{n:n}\) is stochastically larger than \(Y_{n:n}\) in terms of the likelihood ratio order, and provide numerical examples to illustrate the results established here.
PubDate: 2016-08-01
DOI: 10.1007/s00184-015-0573-5
Issue No: Vol. 79, No. 6 (2016)
- Authors: Longxiang Fang; N. Balakrishnan
- On multi-step MLE-process for Markov sequences
- Authors: Yu. A. Kutoyants; A. Motrunich
Pages: 705 - 724
Abstract: Abstract We consider the problem of the construction of the estimator-process of the unknown finite-dimensional parameter in the case of the observations of nonlinear autoregressive process. The estimation is done in two or three steps. First we estimate the unknown parameter by a learning relatively short part of observations and then we use the one-step MLE idea to construct an-estimator process which is asymptotically equivalent to the MLE. To have the learning interval shorter we introduce the two-step procedure which leads to the asymptotically efficient estimator-process too. The presented results are illustrated with the help of two numerical examples.
PubDate: 2016-08-01
DOI: 10.1007/s00184-015-0574-4
Issue No: Vol. 79, No. 6 (2016)
- Authors: Yu. A. Kutoyants; A. Motrunich
- On the records of multivariate random sequences
- Authors: Ismihan Bayramoglu
Pages: 725 - 747
Abstract: Abstract Two types of records in multivariate sequences are considered in this paper. According to the first definition, a multivariate observation is accepted as a record if it is not dominated in at least one of the coordinates of previous record and the first observation is a record. Some basic straightforward results concerning the distributions of record times and records according to this definition are given. The development of distribution theory for these types of record and also providing examples with available analytical results still involves challenging unsolved problems. Second, we consider records of bivariate sequences according to conditionally N-ordering, introduced in Bairamov (J Multivar Anal 97:797–809, 2006). The joint distributions of record times and distributions of record values are derived. Some examples, with particular underlying distributions demonstrating the availability of obtained formulae are provided.
PubDate: 2016-08-01
DOI: 10.1007/s00184-016-0575-y
Issue No: Vol. 79, No. 6 (2016)
- Authors: Ismihan Bayramoglu
- Multivariate Poisson distributions associated with Boolean models
- Authors: Christian Bräu; Lothar Heinrich
Pages: 749 - 761
Abstract: Abstract We consider a d-dimensional Boolean model \(\varXi = (\varXi _1+X_1)\cup (\varXi _2+X_2)\cup \cdots \) generated by a Poisson point process \(\{X_i, i\ge 1\}\) with intensity measure \(\varLambda \) and a sequence \(\{\varXi _i, i\ge 1\}\) of independent copies of some random compact set \(\varXi _0\,\) . Given compact sets \(K_1,\ldots ,K_{\ell }\) , we show that the discrete random vector \((N(K_1),\ldots ,N(K_\ell ))\) , where \(N(K_j)\) equals the number of shifted sets \(\varXi _i+X_i\) hitting \(K_j\) , obeys an \(\ell \) -variate Poisson distribution with \(2^{\ell }-1\) parameters. We obtain explicit formulae for all these parameters which can be estimated consistently from an observation of the union set \(\varXi \) in some unboundedly expanding window \(W_n\) (as \(n \rightarrow \infty \) ) provided that the Boolean model is stationary. Some of these results can be extended to unions of Poisson k-cylinders for \(1\le k < d\) and more general set-valued functionals of independently marked Poisson processes.
PubDate: 2016-08-01
DOI: 10.1007/s00184-016-0576-x
Issue No: Vol. 79, No. 6 (2016)
- Authors: Christian Bräu; Lothar Heinrich
- Robust Dickey–Fuller tests based on ranks for time series with
additive outliers- Authors: V. A. Reisen; C. Lévy-Leduc; M. Bourguignon; H. Boistard
Abstract: Abstract In this paper the unit root tests proposed by Dickey and Fuller (DF) and their rank counterpart suggested by Breitung and Gouriéroux (J Econom 81(1): 7–27, 1997) (BG) are analytically investigated under the presence of additive outlier (AO) contaminations. The results show that the limiting distribution of the former test is outlier dependent, while the latter one is outlier free. The finite sample size properties of these tests are also investigated under different scenarios of testing contaminated unit root processes. In the empirical study, the alternative DF rank test suggested in Granger and Hallman (J Time Ser Anal 12(3): 207–224, 1991) (GH) is also considered. In Fotopoulos and Ahn (J Time Ser Anal 24(6): 647–662, 2003), these unit root rank tests were analytically and empirically investigated and compared to the DF test, but with outlier-free processes. Thus, the results provided in this paper complement the studies of the previous works, but in the context of time series with additive outliers. Equivalently to DF and Granger and Hallman (J Time Ser Anal 12(3): 207–224, 1991) unit root tests, the BG test shows to be sensitive to AO contaminations, but with less severity. In practical situations where there would be a suspicion of additive outlier, the general conclusion is that the DF and Granger and Hallman (J Time Ser Anal 12(3): 207–224, 1991) unit root tests should be avoided, however, the BG approach can still be used.
PubDate: 2016-09-10
DOI: 10.1007/s00184-016-0594-8
- Authors: V. A. Reisen; C. Lévy-Leduc; M. Bourguignon; H. Boistard
- Asymptotics of self-weighted M-estimators for autoregressive models
- Authors: Xinghui Wang; Shuhe Hu
Abstract: Abstract In this paper, we consider a stationary autoregressive AR(p) time series \(y_t=\phi _0+\phi _1y_{t-1}+\cdots +\phi _{p}y_{t-p}+u_t\) . A self-weighted M-estimator for the AR(p) model is proposed. The asymptotic normality of this estimator is established, which includes the asymptotic properties under the innovations with finite or infinite variance. The result generalizes and improves the known one in the literature.
PubDate: 2016-09-09
DOI: 10.1007/s00184-016-0592-x
- Authors: Xinghui Wang; Shuhe Hu
- One-sided hyperbolic simultaneous confidence bands for multiple and
polynomial regression models- Authors: Sanyu Zhou
Abstract: Abstract A simultaneous confidence band is a useful statistical tool in a simultaneous inference procedure. In recent years several papers were published that consider various applications of simultaneous confidence bands, see for example Al-Saidy et al. (Biometrika 59:1056–1062, 2003), Liu et al. (J Am Stat Assoc 99:395–403, 2004), Piegorsch et al. (J R Stat Soc 54:245–258, 2005) and Liu et al. (Aust N Z J Stat 55(4):421–434, 2014). In this article, we provide methods for constructing one-sided hyperbolic imultaneous confidence bands for both the multiple regression model over a rectangular region and the polynomial regression model over an interval. These methods use numerical quadrature. Examples are included to illustrate the methods. These approaches can be applied to more general regression models such as fixed-effect or random-effect generalized linear regression models to construct large sample approximate one-sided hyperbolic simultaneous confidence bands.
PubDate: 2016-09-09
DOI: 10.1007/s00184-016-0598-4
- Authors: Sanyu Zhou
- A new approach to distribution free tests in contingency tables
- Authors: Thuong T. M. Nguyen
Abstract: Abstract We suggest an extremely wide class of asymptotically distribution free goodness of fit tests for testing independence in two-way contingency tables, or equivalently, independence of two discrete random variables. The nature of these tests is that the test statistics can be viewed as definite functions of the transformation of \(\widehat{T}_n = (\widehat{T}_{ij})=\Big (\frac{\nu _{ij}- n\hat{a}_i\hat{b}_j}{\sqrt{n\hat{a}_i\hat{b}_j}}\Big )\) where \(\nu _{ij}\) are frequencies and \(\hat{a}_i, \hat{b}_j\) are estimated marginal distributions. Our method is also applicable for testing independence of two discrete random vectors. We make some comparisons on statistical powers of the new tests with the conventional chi-square test and suggest some cases in which this class is significantly more powerful.
PubDate: 2016-09-08
DOI: 10.1007/s00184-016-0596-6
- Authors: Thuong T. M. Nguyen
- Model misspecification effects for biased samples
- Authors: George Tzavelas; Maria Douli; Polychronis Economou
Abstract: Abstract The model misspecification effects on the maximum likelihood estimator are studied when a biased sample is treated as a random one as well as when a random sample is treated as a biased one. The relation between the existence of a consistent estimator under model misspecification and the completeness of the distribution is also considered. The cases of the weight invariant distribution and the scale parameter distribution are examined and finally an example is presented to illustrate the results.
PubDate: 2016-09-07
DOI: 10.1007/s00184-016-0597-5
- Authors: George Tzavelas; Maria Douli; Polychronis Economou
- Fiducial inference in the classical errors-in-variables model
- Authors: Liang Yan; Rui Wang; Xingzhong Xu
Abstract: Abstract For the slope parameter of the classical errors-in-variables model, existing interval estimations with finite length will have confidence level equal to zero because of the Gleser–Hwang effect. Especially when the reliability ratio is low and the sample size is small, the Gleser–Hwang effect is so serious that it leads to the very liberal coverages and the unacceptable lengths of the existing confidence intervals. In this paper, we obtain two new fiducial intervals for the slope. One is based on a fiducial generalized pivotal quantity and we prove that this interval has the correct asymptotic coverage. The other fiducial interval is based on the method of the generalized fiducial distribution. We also construct these two fiducial intervals for the other parameters of interest of the classical errors-in-variables model and introduce these intervals to a hybrid model. Then, we compare these two fiducial intervals with the existing intervals in terms of empirical coverage and average length. Simulation results show that the two proposed fiducial intervals have better frequency performance. Finally, we provide a real data example to illustrate our approaches.
PubDate: 2016-09-07
DOI: 10.1007/s00184-016-0593-9
- Authors: Liang Yan; Rui Wang; Xingzhong Xu
- Shrinkage estimation of the linear model with spatial interaction
- Authors: Yueqin Wu; Yan Sun
Abstract: Abstract The linear model with spatial interaction has attracted huge attention in the past several decades. Different from most existing research which focuses on its estimation, we study its variable selection problem using the adaptive lasso. Our results show that the method can identify the true model consistently, and the resulting estimator can be efficient as the oracle estimator which is obtained when the zero coefficients in the model are known. Simulation studies show that the proposed methods perform very well.
PubDate: 2016-08-13
DOI: 10.1007/s00184-016-0590-z
- Authors: Yueqin Wu; Yan Sun
- On the residual lifetime of coherent systems with heterogeneous components
- Authors: P. Samadi; M. Rezaei; M. Chahkandi
Abstract: Abstract The residual lifetime is of significant interest in reliability and survival analysis. In this article, we obtain a mixture representation for the reliability function of the residual lifetime of a coherent system with heterogeneous components in terms of the reliability functions of residual lifetimes of order statistics. Some stochastic comparisons are made on the residual lifetimes of the systems. Some examples are also given to illustrate the main results.
PubDate: 2016-08-11
DOI: 10.1007/s00184-016-0591-y
- Authors: P. Samadi; M. Rezaei; M. Chahkandi