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] |
- Blocked factor aliased effect-number pattern and column rank of blocked
regular designs- Authors: Dongying Wang; Shili Ye; Qi Zhou; Runchu Zhang
Pages: 133 - 152
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: 2017-02-01
DOI: 10.1007/s00184-016-0595-7
Issue No: Vol. 80, No. 2 (2017)
- Authors: Dongying Wang; Shili Ye; Qi Zhou; Runchu Zhang
- A new approach to distribution free tests in contingency tables
- Authors: Thuong T. M. Nguyen
Pages: 153 - 170
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: 2017-02-01
DOI: 10.1007/s00184-016-0596-6
Issue No: Vol. 80, No. 2 (2017)
- Authors: Thuong T. M. Nguyen
- Model misspecification effects for biased samples
- Authors: George Tzavelas; Maria Douli; Polychronis Economou
Pages: 171 - 185
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: 2017-02-01
DOI: 10.1007/s00184-016-0597-5
Issue No: Vol. 80, No. 2 (2017)
- Authors: George Tzavelas; Maria Douli; Polychronis Economou
- One-sided hyperbolic simultaneous confidence bands for multiple and
polynomial regression models- Authors: Sanyu Zhou
Pages: 187 - 200
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: 2017-02-01
DOI: 10.1007/s00184-016-0598-4
Issue No: Vol. 80, No. 2 (2017)
- Authors: Sanyu Zhou
- Barycentric algorithm for computing D-optimal size- and cost-constrained
designs of experiments- Authors: Radoslav Harman; Eva Benková
Pages: 201 - 225
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: 2017-02-01
DOI: 10.1007/s00184-016-0599-3
Issue No: Vol. 80, No. 2 (2017)
- Authors: Radoslav Harman; Eva Benková
- Notes on consistency of some minimum distance estimators with simulation
results- Authors: Jitka Hrabáková; Václav Kůs
Pages: 243 - 257
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: 2017-02-01
DOI: 10.1007/s00184-016-0601-0
Issue No: Vol. 80, No. 2 (2017)
- Authors: Jitka Hrabáková; Václav Kůs
- Conditional empirical likelihood for quantile regression models
- Authors: Wu Wang; Zhongyi Zhu
Pages: 1 - 16
Abstract: In this paper, we propose a new Bayesian quantile regression estimator using conditional empirical likelihood as the working likelihood function. We show that the proposed estimator is asymptotically efficient and the confidence interval constructed is asymptotically valid. Our estimator has low computation cost since the posterior distribution function has explicit form. The finite sample performance of the proposed estimator is evaluated through Monte Carlo studies.
PubDate: 2017-01-01
DOI: 10.1007/s00184-016-0588-6
Issue No: Vol. 80, No. 1 (2017)
- Authors: Wu Wang; Zhongyi Zhu
- Robust feature screening for varying coefficient models via quantile
partial correlation- Authors: Xiang-Jie Li; Xue-Jun Ma; Jing-Xiao Zhang
Pages: 17 - 49
Abstract: This article is concerned with feature screening for varying coefficient models with ultrahigh-dimensional predictors. We propose a new sure independence screening method based on quantile partial correlation (QPC-SIS), which is quite robust against outliers and heavy-tailed distributions. Then we establish the sure screening property for the QPC-SIS, and conduct simulations to examine its finite sample performance. The results of simulation study indicate that the QPC-SIS performs better than other methods like sure independent screening (SIS), sure independent ranking and screening, distance correlation-sure independent screening, conditional correlation sure independence screening and nonparametric independent screening, which shows the validity and rationality of QPC-SIS.
PubDate: 2017-01-01
DOI: 10.1007/s00184-016-0589-5
Issue No: Vol. 80, No. 1 (2017)
- Authors: Xiang-Jie Li; Xue-Jun Ma; Jing-Xiao Zhang
- Shrinkage estimation of the linear model with spatial interaction
- Authors: Yueqin Wu; Yan Sun
Pages: 51 - 68
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: 2017-01-01
DOI: 10.1007/s00184-016-0590-z
Issue No: Vol. 80, No. 1 (2017)
- Authors: Yueqin Wu; Yan Sun
- On the residual lifetime of coherent systems with heterogeneous components
- Authors: P. Samadi; M. Rezaei; M. Chahkandi
Pages: 69 - 82
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: 2017-01-01
DOI: 10.1007/s00184-016-0591-y
Issue No: Vol. 80, No. 1 (2017)
- Authors: P. Samadi; M. Rezaei; M. Chahkandi
- Asymptotics of self-weighted M-estimators for autoregressive models
- Authors: Xinghui Wang; Shuhe Hu
Pages: 83 - 92
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: 2017-01-01
DOI: 10.1007/s00184-016-0592-x
Issue No: Vol. 80, No. 1 (2017)
- Authors: Xinghui Wang; Shuhe Hu
- Fiducial inference in the classical errors-in-variables model
- Authors: Liang Yan; Rui Wang; Xingzhong Xu
Pages: 93 - 114
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: 2017-01-01
DOI: 10.1007/s00184-016-0593-9
Issue No: Vol. 80, No. 1 (2017)
- Authors: Liang Yan; Rui Wang; Xingzhong Xu
- Robust Dickey–Fuller tests based on ranks for time series with
additive outliers- Authors: V. A. Reisen; C. Lévy-Leduc; M. Bourguignon; H. Boistard
Pages: 115 - 131
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: 2017-01-01
DOI: 10.1007/s00184-016-0594-8
Issue No: Vol. 80, No. 1 (2017)
- Authors: V. A. Reisen; C. Lévy-Leduc; M. Bourguignon; H. Boistard
- The variance of the discrepancy distribution of rounding procedures, and
sums of uniform random variables- Authors: Lothar Heinrich; Friedrich Pukelsheim; Vitali Wachtel
Abstract: When \(\ell \) probabilities are rounded to integer multiples of a given accuracy n, the sum of the numerators may deviate from n by a nonzero discrepancy. It is proved that, for large accuracies \(n \rightarrow \infty \) , the limiting discrepancy distribution has variance \(\ell /12\) . The relation to the uniform distribution over the interval \([-1/2, 1/2]\) , whose variance is 1 / 12, is explored in detail.
PubDate: 2017-01-19
DOI: 10.1007/s00184-017-0609-0
- Authors: Lothar Heinrich; Friedrich Pukelsheim; Vitali Wachtel
- Nonparametric estimation for self-selected interval data collected through
a two-stage approach- Authors: Angel G. Angelov; Magnus Ekström
Abstract: Self-selected interval data arise in questionnaire surveys when respondents are free to answer with any interval without having pre-specified ranges. This type of data is a special case of interval-censored data in which the assumption of noninformative censoring is violated, and thus the standard methods for interval-censored data (e.g. Turnbull’s estimator) are not appropriate because they can produce biased results. Based on a certain sampling scheme, this paper suggests a nonparametric maximum likelihood estimator of the underlying distribution function. The consistency of the estimator is proven under general assumptions, and an iterative procedure for finding the estimate is proposed. The performance of the method is investigated in a simulation study.
PubDate: 2017-01-16
DOI: 10.1007/s00184-017-0610-7
- Authors: Angel G. Angelov; Magnus Ekström
- Bayesian estimation based on ranked set sample from Morgenstern type
bivariate exponential distribution when ranking is imperfect- Authors: Manoj Chacko
Abstract: In this paper we consider Bayes estimation based on ranked set sample when ranking is imperfect, in which units are ranked based on measurements made on an easily and exactly measurable auxiliary variable X which is correlated with the study variable Y. Bayes estimators under squared error loss function and LINEX loss function for the mean of the study variate Y, when (X, Y) follows a Morgenstern type bivariate exponential distribution, are obtained based on both usual ranked set sample and extreme ranked set sample. Estimation procedures developed in this paper are illustrated using simulation studies and a real data.
PubDate: 2016-12-08
DOI: 10.1007/s00184-016-0607-7
- Authors: Manoj Chacko
- On the shape of the cross-ratio function in bivariate survival models
induced by truncated and folded normal frailty distributions- Authors: Steffen Unkel
Abstract: In shared frailty models for bivariate survival data the frailty is identifiable through the cross-ratio function (CRF), which provides a convenient measure of association for correlated survival variables. The CRF may be used to compare patterns of dependence across models and data sets. We explore the shape of the CRF for the families of one-sided truncated normal and folded normal frailty distributions.
PubDate: 2016-12-07
DOI: 10.1007/s00184-016-0608-6
- Authors: Steffen Unkel
- An ergodic theorem for proportions of observations that fall into random
sets determined by sample quantiles- Authors: Anna Dembińska
Abstract: Assume that a sequence of observations \((X_n; n\ge 1)\) forms a strictly stationary process with an arbitrary univariate cumulative distribution function. We investigate almost sure asymptotic behavior of proportions of observations in the sample that fall into a random region determined by a given Borel set and a sample quantile. We provide sufficient conditions under which these proportions converge almost surly and describe the law of the limiting random variable.
PubDate: 2016-12-07
DOI: 10.1007/s00184-016-0606-8
- Authors: Anna Dembińska
- Acceleration of the stochastic search variable selection via componentwise
Gibbs sampling- Authors: Hengzhen Huang; Shuangshuang Zhou; Min-Qian Liu; Zong-Feng Qi
Abstract: The stochastic search variable selection proposed by George and McCulloch (J Am Stat Assoc 88:881–889, 1993) is one of the most popular variable selection methods for linear regression models. Many efforts have been proposed in the literature to improve its computational efficiency. However, most of these efforts change its original Bayesian formulation, thus the comparisons are not fair. This work focuses on how to improve the computational efficiency of the stochastic search variable selection, but remains its original Bayesian formulation unchanged. The improvement is achieved by developing a new Gibbs sampling scheme different from that of George and McCulloch (J Am Stat Assoc 88:881–889, 1993). A remarkable feature of the proposed Gibbs sampling scheme is that, it samples the regression coefficients from their posterior distributions in a componentwise manner, so that the expensive computation of the inverse of the information matrix, which is involved in the algorithm of George and McCulloch (J Am Stat Assoc 88:881–889, 1993), can be avoided. Moreover, since the original Bayesian formulation remains unchanged, the stochastic search variable selection using the proposed Gibbs sampling scheme shall be as efficient as that of George and McCulloch (J Am Stat Assoc 88:881–889, 1993) in terms of assigning large probabilities to those promising models. Some numerical results support these findings.
PubDate: 2016-11-22
DOI: 10.1007/s00184-016-0604-x
- Authors: Hengzhen Huang; Shuangshuang Zhou; Min-Qian Liu; Zong-Feng Qi
- A study on the conditional inactivity time of coherent systems
- Authors: S. Goli; M. Asadi
Abstract: The study on the inactivity times is useful in evaluating the aging and reliability properties of coherent systems in reliability engineering. In the present paper, we investigate the inactivity time of a coherent system consisting of n i.i.d. components. We drive some mixture representations for the reliability function of conditional inactivity times of coherent systems under two specific conditions on the status of the system components. Some ageing and stochastic properties of the proposed conditional inactivity times are also explored.
PubDate: 2016-10-25
DOI: 10.1007/s00184-016-0600-1
- Authors: S. Goli; M. Asadi