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 [2336 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
- Imputation based statistical inference for partially linear quantile
regression models with missing responses- Authors: Peixin Zhao; Xinrong Tang
Abstract: Abstract In this paper, we consider the confidence interval construction for partially linear quantile regression models with missing response at random. We propose an imputation based empirical likelihood method to construct confidence intervals for the parametric components and the nonparametric components, and show that the proposed empirical log-likelihood ratios are both asymptotically Chi-squared in theory. Then, the confidence region for the parametric component and the pointwise confidence interval for the nonparametric component are constructed. Some simulation studies and a real data application are carried out to assess the performance of the proposed estimation method, and simulation results indicate that the proposed method is workable.
PubDate: 2016-11-01
DOI: 10.1007/s00184-016-0586-8
- Authors: Peixin Zhao; Xinrong Tang
- Qualitative robustness of estimators on stochastic processes
- Authors: Katharina Strohriegl; Robert Hable
Abstract: Abstract A lot of statistical methods originally designed for independent and identically distributed (i.i.d.) data are also successfully used for dependent observations. Still most theoretical investigations on robustness assume i.i.d. pairs of random variables. We examine an important property of statistical estimators—the qualitative robustness in the case of observations which do not fulfill the i.i.d. assumption. In the i.i.d. case qualitative robustness of a sequence of estimators is, according to Hampel (Ann Math Stat 42:1887–1896, 1971), ensured by continuity of the corresponding statistical functional. A similar result for the non-i.i.d. case is shown in this article. Continuity of the corresponding statistical functional still ensures qualitative robustness of the estimator as long as the data generating process satisfies a certain convergence condition on its empirical measure. Examples for processes providing such a convergence condition, including certain Markov chains or mixing processes, are given as well as examples for qualitatively robust estimators in the non-i.i.d. case.
PubDate: 2016-11-01
DOI: 10.1007/s00184-016-0582-z
- Authors: Katharina Strohriegl; Robert Hable
- Tree based diagnostic procedures following a smooth test of
goodness-of-fit- Authors: Gilles R. Ducharme; Walid Al Akhras
Abstract: Abstract This paper introduces a statistical procedure, to be applied after a goodness-of-fit test has rejected a null model, that provides diagnostic information to help the user decide on a better model. The procedure goes through a list of departures, each being tested by a local smooth test. The list is organized into a hierarchy by seeking answers to the questions “Where is the problem?” and “What is the problem there?”. This hierarchy allows to focus on finer departures as the data becomes more abundant. The procedure controls the family-wise Type 1 error rate. Simulations show that the procedure can succeed in providing useful diagnostic information.
PubDate: 2016-11-01
DOI: 10.1007/s00184-016-0585-9
- Authors: Gilles R. Ducharme; Walid Al Akhras
- A test of linearity in partial functional linear regression
- Authors: Ping Yu; Zhongzhan Zhang; Jiang Du
Abstract: Abstract This paper investigates the hypothesis test of the parametric component in partial functional linear regression. We propose a test procedure based on the residual sums of squares under the null and alternative hypothesis, and establish the asymptotic properties of the resulting test. A simulation study shows that the proposed test procedure has good size and power with finite sample sizes. Finally, we present an illustration through fitting the Berkeley growth data with a partial functional linear regression model and testing the effect of gender on the height of kids.
PubDate: 2016-11-01
DOI: 10.1007/s00184-016-0584-x
- Authors: Ping Yu; Zhongzhan Zhang; Jiang Du
- AR(1) model with skew-normal innovations
- Authors: M. Sharafi; A. R. Nematollahi
Abstract: Abstract In this paper, we consider an autoregressive model of order one with skew-normal innovations. We propose several methods for estimating the parameters of the model and derive the limiting distributions of the estimators. Then, we study some statistical properties and the regression behavior of the proposed model. Finally, we provide a Monte Carlo simulation study for comparing performance of estimators and consider a real time series to illustrate the applicability of the proposed model.
PubDate: 2016-11-01
DOI: 10.1007/s00184-016-0587-7
- Authors: M. Sharafi; A. R. Nematollahi
- Nonparametric estimation in a mixed-effect Ornstein–Uhlenbeck model
- Authors: Charlotte Dion
Abstract: Abstract Two adaptive nonparametric procedures are proposed to estimate the density of the random effects in a mixed-effect Ornstein–Uhlenbeck model. First a kernel estimator is introduced with a new bandwidth selection method developed recently by Goldenshluger and Lepski (Ann Stat 39:1608–1632, 2011). Then, we adapt an estimator from Comte et al. (Stoch Process Appl 7:2522–2551, 2013) in the framework of small time interval of observation. More precisely, we propose an estimator that uses deconvolution tools and depends on two tuning parameters to be chosen in a data-driven way. The selection of these two parameters is achieved through a two-dimensional penalized criterion. For both adaptive estimators, risk bounds are provided in terms of integrated \(\mathbb {L}^2\) -error. The estimators are evaluated on simulations and show good results. Finally, these nonparametric estimators are applied to neuronal data and are compared with previous parametric estimations.
PubDate: 2016-11-01
DOI: 10.1007/s00184-016-0583-y
- Authors: Charlotte Dion
- Barycentric algorithm for computing D-optimal size- and cost-constrained
designs of experiments- Authors: Radoslav Harman; Eva Benková
Abstract: Abstract In this paper, we study the problem of D-optimal experimental design under two linear constraints, which can be interpreted as simultaneous restrictions on the size and on the cost of the experiment. For computing a size- and cost-constrained approximate D-optimal design, we propose a specification of the “barycentric” multiplicative algorithm with sequential removal of redundant design points. We analytically prove convergence results for the proposed algorithm and numerically demonstrate its favorable properties compared to competing methods.
PubDate: 2016-10-19
DOI: 10.1007/s00184-016-0599-3
- Authors: Radoslav Harman; Eva Benková
- Notes on consistency of some minimum distance estimators with simulation
results- Authors: Jitka Hrabáková; Václav Kůs
Abstract: Abstract We focus on the minimum distance density estimators \({\widehat{f}}_n\) of the true probability density \(f_0\) on the real line. The consistency of the order of \(n^{-1/2}\) in the (expected) L \(_1\) -norm of Kolmogorov estimator (MKE) is known if the degree of variations of the nonparametric family \(\mathcal {D}\) is finite. Using this result for MKE we prove that minimum Lévy and minimum discrepancy distance estimators are consistent of the order of \(n^{-1/2}\) in the (expected) L \(_1\) -norm under the same assumptions. Computer simulation for these minimum distance estimators, accompanied by Cramér estimator, is performed and the function \(s(n)=a_0+a_1\sqrt{n}\) is fitted to the L \(_1\) -errors of \({\widehat{f}}_n\) leading to the proportionality constant \(a_1\) determination. Further, (expected) L \(_1\) -consistency rate of Kolmogorov estimator under generalized assumptions based on asymptotic domination relation is studied. No usual continuity or differentiability conditions are needed.
PubDate: 2016-10-18
DOI: 10.1007/s00184-016-0601-0
- Authors: Jitka Hrabáková; Václav Kůs
- The concept of weak exchangeability and its applications
- Authors: Serkan Eryilmaz
Abstract: Abstract A finite sequence of binary random variables is called a weak exchangeable sequence of order m if the sequence consists of m random vectors such that the elements within each random vector are exchangeable in the usual sense and the different random vectors are dependent. The exact and asymptotic joint distributions of the m-dimensional random vector whose elements include the number of successes in each exchangeable sequence are derived. Potential applications of the concept of weak exchangeability are discussed with illustrative examples.
PubDate: 2016-10-17
DOI: 10.1007/s00184-016-0602-z
- Authors: Serkan Eryilmaz
- Blocked factor aliased effect-number pattern and column rank of blocked
regular designs- Authors: Dongying Wang; Shili Ye; Qi Zhou; Runchu Zhang
Abstract: Abstract In factorial experiments, estimation precision of specific factor effects depends not only on design selection but also on factor assignments to columns of selected designs. Usually, different columns in a design play different roles when estimating factor effects. Zhou et al. (Can J Stat 41:540-555, 2013) introduced a factor aliased effect-number pattern (F-AENP) and proposed a column ranking scheme for all the GMC \(2^{n-m}\) designs with \(5N/16+1\le n\le N-1\) , where \(N=2^{n-m}\) . In this paper, we first introduce a blocked factor aliased effect-number pattern (B-F-AENP) for blocked regular designs as an extension of the F-AENP. Then, by using the B-F-AENP, we propose a column ranking scheme for all the B \(^1\) -GMC \(2^{n-m}:2^s\) designs with \(5N/16+1\le n\le N-1\) , as well as an assignment strategy for important factors.
PubDate: 2016-09-30
DOI: 10.1007/s00184-016-0595-7
- Authors: Dongying Wang; Shili Ye; Qi Zhou; Runchu Zhang
- 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