Metrika [SJR: 0.943] [H-I: 25] [2 followers] Follow Hybrid journal (It can contain Open Access articles) ISSN (Print) 1435-926X - ISSN (Online) 0026-1335 Published by Springer-Verlag [2334 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
- Asymptotic results of a nonparametric conditional cumulative distribution
estimator in the single functional index modeling for time series data
with applications- Authors: Said Attaoui; Nengxiang Ling
Pages: 485 - 511
Abstract: Abstract In this paper, we treat nonparametric estimation of the conditional cumulative distribution with a scalar response variable conditioned by a functional Hilbertian regressor. We establish asymptotic normality and uniform almost complete convergence rates of the conditional cumulative distribution estimator for dependent variables, linked semiparametrically by the single index structure. Furthermore, we provide some applications and simulations to illustrate our methodology.
PubDate: 2016-07-01
DOI: 10.1007/s00184-015-0564-6
Issue No: Vol. 79, No. 5 (2016)
- Authors: Said Attaoui; Nengxiang Ling
- A mixture model of size-biased distributions
- Authors: M. Kayid; S. Izadkhah; J. Jarrahiferiz; P. Asghari
Pages: 513 - 529
Abstract: Abstract In reliability and survival analysis, to model lifetime data, size-biased distributions are useful. In this paper, a mixture model of size-biased distributions is introduced and studied. Several reliability properties of this model are investigated. In addition, some implications of well-known stochastic orders and aging classes concerning the model are established. To underline the usefulness of the model, some examples of interest in reliability and statistics are given.
PubDate: 2016-07-01
DOI: 10.1007/s00184-015-0565-5
Issue No: Vol. 79, No. 5 (2016)
- Authors: M. Kayid; S. Izadkhah; J. Jarrahiferiz; P. Asghari
- Single change-point detection methods for small lifetime samples
- Authors: Narayanaswamy Balakrishnan; Laurent Bordes; Christian Paroissin; Jean-Christophe Turlot
Pages: 531 - 551
Abstract: Abstract In this paper, we address the problem of deciding if either n consecutive independent failure times have the same failure rate or if there exists some \(k\in \{1,\ldots ,n\}\) such that the common failure rate of the first k failure times is different from the common failure rate of the last \(n-k\) failure times, based on an exponential lifetime distribution. The statistical test we propose is based on the empirical average ratio under the assumption of exponentiality. The proposed test is compared to the one based on the Mann–Whitney statistic for which no parametric assumption on the underlying distribution is necessary. The proposed statistics are free of the unknown underlying distribution under the null hypothesis of homogeneity of the n failure times which enables the determination of critical values of the proposed tests by Monte Carlo methods for small sample sizes.
PubDate: 2016-07-01
DOI: 10.1007/s00184-015-0566-4
Issue No: Vol. 79, No. 5 (2016)
- Authors: Narayanaswamy Balakrishnan; Laurent Bordes; Christian Paroissin; Jean-Christophe Turlot
- Stochastic somparisons of order statistics from scaled and interdependent
random variables- Authors: Chen Li; Rui Fang; Xiaohu Li
Pages: 553 - 578
Abstract: Abstract This paper studies order statistics from random variables following the scale model. In the presence of the Archimedean copula or survival copula for the random variables, we obtain the usual stochastic order of the sample extremes and the second smallest order statistic, the dispersive order and the star order of the sample extremes.
PubDate: 2016-07-01
DOI: 10.1007/s00184-015-0567-3
Issue No: Vol. 79, No. 5 (2016)
- Authors: Chen Li; Rui Fang; Xiaohu Li
- On runs of ones defined on a q -sequence of binary trials
- Authors: Frosso S. Makri; Zaharias M. Psillakis
Pages: 579 - 602
Abstract: Abstract In a sequence of n binary ( \(0{-}1\) ) trials, with probability of ones varying according to a geometric rule, we consider a random variable denoting the number of runs of ones of length at least equal to a fixed threshold k, \(1\le k\le n\) . Closed and recursive expressions are obtained for the probability mass function, generating functions and moments of this random variable. Statistical inference problems related to the probability of ones are examined by numerical techniques. Numerics illustrate further the theoretical results.
PubDate: 2016-07-01
DOI: 10.1007/s00184-015-0568-2
Issue No: Vol. 79, No. 5 (2016)
- Authors: Frosso S. Makri; Zaharias M. Psillakis
- A new method of kernel-smoothing estimation of the ROC curve
- Authors: Michał Pulit
Pages: 603 - 634
Abstract: Abstract The receiver operating characteristic (ROC) curve is a popular graphical tool for describing the accuracy of a diagnostic test. Based on the idea of estimating the ROC curve as a distribution function, we propose a new kernel smoothing estimator of the ROC curve which is invariant under nondecreasing data transformations. We prove that the estimator has better asymptotic mean squared error properties than some other estimators involving kernel smoothing and we present an easy method of bandwidth selection. By simulation studies, we show that for the limited sample sizes, our proposed estimator is competitive with some other nonparametric estimators of the ROC curve. We also give an example of applying the estimator to a real data set.
PubDate: 2016-07-01
DOI: 10.1007/s00184-015-0569-1
Issue No: Vol. 79, No. 5 (2016)
- Authors: Michał Pulit
- 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