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 [2341 journals] |
- Nonparametric estimation for self-selected interval data collected through
a two-stage approach- Authors: Angel G. Angelov; Magnus Ekström
Pages: 377 - 399
Abstract: 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: 2017-05-01
DOI: 10.1007/s00184-017-0610-7
Issue No: Vol. 80, No. 4 (2017)
- Authors: Angel G. Angelov; Magnus Ekström
- The concept of weak exchangeability and its applications
- Authors: Serkan Eryilmaz
Pages: 259 - 271
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: 2017-04-01
DOI: 10.1007/s00184-016-0602-z
Issue No: Vol. 80, No. 3 (2017)
- Authors: Serkan Eryilmaz
- Reliability parameters estimation for parallel systems under imperfect
repair- Authors: Soumaya Ghnimi; Soufiane Gasmi; Arwa Nasr
Pages: 273 - 288
Abstract: Abstract We consider in this paper a parallel system consisting of \(\eta \) identical components. Each component works independently of the others and has a Weibull distributed inter-failure time. When the system fails, we assume that the repair maintenance is imperfect according to the Arithmetic Reduction of Age models ( \(ARA_{m}\) ) proposed by Doyen and Gaudoin. The purpose of this paper is to generate a simulated failure data of the whole system in order to forecast the behavior of the failure process. Besides, we estimate the maintenance efficiency and the reliability parameters of an imperfect repair following \(ARA_{m}\) models using maximum likelihood estimation method. Our method is tested with several data sets available from related sources. The real data set corresponds to the time between failures of a compressor which is tested by Likelihood Ratio Test (LR). An analysis of the importance and the effect of the memory order of imperfect repair classes ( \(ARA_{m}\) ) will be discussed using LR test.
PubDate: 2017-04-01
DOI: 10.1007/s00184-016-0603-y
Issue No: Vol. 80, No. 3 (2017)
- Authors: Soumaya Ghnimi; Soufiane Gasmi; Arwa Nasr
- Acceleration of the stochastic search variable selection via componentwise
Gibbs sampling- Authors: Hengzhen Huang; Shuangshuang Zhou; Min-Qian Liu; Zong-Feng Qi
Pages: 289 - 308
Abstract: 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: 2017-04-01
DOI: 10.1007/s00184-016-0604-x
Issue No: Vol. 80, No. 3 (2017)
- Authors: Hengzhen Huang; Shuangshuang Zhou; Min-Qian Liu; Zong-Feng Qi
- Efficient paired choice designs with fewer choice pairs
- Authors: Aloke Dey; Rakhi Singh; Ashish Das
Pages: 309 - 317
Abstract: Abstract For paired choice experiments, two new construction methods of designs are proposed for the estimation of the main effects. In many cases, these designs require about 30–50% fewer choice pairs than the existing designs and at the same time have reasonably high D-efficiencies for the estimation of the main effects. Furthermore, as against the existing efficient designs, our designs have higher D-efficiencies for the same number of choice pairs.
PubDate: 2017-04-01
DOI: 10.1007/s00184-016-0605-9
Issue No: Vol. 80, No. 3 (2017)
- Authors: Aloke Dey; Rakhi Singh; Ashish Das
- 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: 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: 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: 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: 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: 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: 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
- Estimation of the order restricted scale parameters for two populations
from the Lomax distribution- Authors: Constantinos Petropoulos
Abstract: Abstract The usual methods of estimating the unknown parameters of a distribution, use only the information given from the sample data. In many cases, there is, also, another important information for estimating the unknown parameters of our model, such as the order of these parameters, and this last information improves the quality of estimation. In this paper, we deal with the problem of estimating the ordered scale parameters from two populations of the multivariate Lomax distribution, with unknown location parameters. It is proved that the best equivariant estimators of the scale parameters (in the unrestricted case) are not admissible and we construct estimators that improve upon the usual ones (when these parameters are known to be ordered).
PubDate: 2017-03-16
DOI: 10.1007/s00184-017-0615-2
- Authors: Constantinos Petropoulos
- Minimum distance estimators for count data based on the probability
generating function with applications- Authors: M. D. Jiménez-Gamero; A. Batsidis
Abstract: Abstract This paper studies properties of parameter estimators obtained by minimizing a distance between the empirical probability generating function and the probability generating function of a model for count data. Specifically, it is shown that, under certain not restrictive conditions, the resulting estimators are consistent and, suitably normalized, asymptotically normal. These properties hold even if the model is misspecified. Three applications of the obtained results are considered. First, we revisit the goodness-of-fit problem for count data and propose a weighted bootstrap estimator of the null distribution of test statistics based on the above cited distance. Second, we give a probability generating function version of the model selection test problem for separate, overlapping and nested families of distributions. Finally, we provide an application to the problem of testing for separate families of distributions. All applications are illustrated with numerical examples.
PubDate: 2017-03-15
DOI: 10.1007/s00184-017-0614-3
- Authors: M. D. Jiménez-Gamero; A. Batsidis
- On bending (down and up) property of reliability measures in mixtures
- Authors: F. G. Badía; Ji Hwan Cha
Abstract: Abstract In this paper, we study the bending property of the failure rate, reversed hazard rate, mean residual life and mean inactivity time in mixtures. For those four reliability measures, the weak and strong bending properties are studied and discussed, respectively. The results are illustrated with suitable examples, where most of them are relative to the model of proportional reliability measures.
PubDate: 2017-03-14
DOI: 10.1007/s00184-017-0613-4
- Authors: F. G. Badía; Ji Hwan Cha
- Estimation in generalized bivariate Birnbaum–Saunders models
- Authors: Helton Saulo; N. Balakrishnan; Xiaojun Zhu; Jhon F. B. Gonzales; Jeremias Leão
Abstract: Abstract In this paper, we propose two moment-type estimation methods for the parameters of the generalized bivariate Birnbaum–Saunders distribution by taking advantage of some properties of the distribution. The proposed moment-type estimators are easy to compute and always exist uniquely. We derive the asymptotic distributions of these estimators and carry out a simulation study to evaluate the performance of all these estimators. The probability coverages of confidence intervals are also discussed. Finally, two examples are used to illustrate the proposed methods.
PubDate: 2017-03-10
DOI: 10.1007/s00184-017-0612-5
- Authors: Helton Saulo; N. Balakrishnan; Xiaojun Zhu; Jhon F. B. Gonzales; Jeremias Leão
- On generalized progressive hybrid censoring in presence of competing risks
- Authors: Arnab Koley; Debasis Kundu
Abstract: Abstract The progressive Type-II hybrid censoring scheme introduced by Kundu and Joarder (Comput Stat Data Anal 50:2509–2528, 2006), has received some attention in the last few years. One major drawback of this censoring scheme is that very few observations (even no observation at all) may be observed at the end of the experiment. To overcome this problem, Cho et al. (Stat Methodol 23:18–34, 2015) recently introduced generalized progressive censoring which ensures to get a pre specified number of failures. In this paper we analyze generalized progressive censored data in presence of competing risks. For brevity we have considered only two competing causes of failures, and it is assumed that the lifetime of the competing causes follow one parameter exponential distributions with different scale parameters. We obtain the maximum likelihood estimators of the unknown parameters and also provide their exact distributions. Based on the exact distributions of the maximum likelihood estimators exact confidence intervals can be obtained. Asymptotic and bootstrap confidence intervals are also provided for comparison purposes. We further consider the Bayesian analysis of the unknown parameters under a very flexible beta–gamma prior. We provide the Bayes estimates and the associated credible intervals of the unknown parameters based on the above priors. We present extensive simulation results to see the effectiveness of the proposed method and finally one real data set is analyzed for illustrative purpose.
PubDate: 2017-02-24
DOI: 10.1007/s00184-017-0611-6
- Authors: Arnab Koley; Debasis Kundu
- The variance of the discrepancy distribution of rounding procedures, and
sums of uniform random variables- Authors: Lothar Heinrich; Friedrich Pukelsheim; Vitali Wachtel
Abstract: 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
- Bayesian estimation based on ranked set sample from Morgenstern type
bivariate exponential distribution when ranking is imperfect- Authors: Manoj Chacko
Abstract: 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: 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: 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