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  Subjects -> STATISTICS (Total: 131 journals)
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Journal Cover Metrika
  [SJR: 0.605]   [H-I: 30]   [3 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1435-926X - ISSN (Online) 0026-1335
   Published by Springer-Verlag Homepage  [2350 journals]
  • Goodness-of-fit tests in linear EV regression with replications
    • Authors: Weijia Jia; Weixing Song
      Pages: 395 - 421
      Abstract: This paper proposes a goodness-of-fit test for checking the adequacy of parametric forms of the regression error density functions in linear errors-in-variables regression models. Instead of assuming the distribution of the measurement error to be known, we assume that replications of the surrogates of the latent variables are available. The test statistic is based upon a weighted integrated squared distance between a nonparametric estimator and a semi-parametric estimator of the density functions of certain residuals. Under the null hypothesis, the test statistic is shown to be asymptotically normal. Consistency and local power results of the proposed test under fixed alternatives and local alternatives are also established. Finite sample performance of the proposed test is evaluated via simulation studies. A real data example is also included to demonstrate an application of the proposed test.
      PubDate: 2018-05-01
      DOI: 10.1007/s00184-018-0648-1
      Issue No: Vol. 81, No. 4 (2018)
  • An algebraic generalisation of some variants of simple correspondence
    • Authors: Eric J. Beh; Rosaria Lombardo
      Pages: 423 - 443
      Abstract: For an analysis of the association between two categorical variables that are cross-classified to form a contingency table, graphical procedures have been central to this analysis. In particular, correspondence analysis has grown to be a popular method for obtaining such a summary and there is a great variety of different approaches that one may consider to perform. In this paper, we shall introduce a simple algebraic generalisation of some of the more common approaches to obtaining a graphical summary of association, where these approaches are akin to the correspondence analysis of a two-way contingency table. Specific cases of the generalised procedure include the classical and non-symmetrical correspondence plots and the symmetrical and isometric biplots.
      PubDate: 2018-05-01
      DOI: 10.1007/s00184-018-0649-0
      Issue No: Vol. 81, No. 4 (2018)
  • Preservation of increasing convex/concave order under the formation of
           parallel/series system of dependent components
    • Authors: Chen Li; Xiaohu Li
      Pages: 445 - 464
      Abstract: This paper investigates sufficient conditions for preservation property of the increasing convex order and the increasing concave order under the taking of maximum and minimum of statistically dependent random variables, respectively. As applications, we develop the preservation of NBUC and NBU(2) aging properties respectively under the parallel and series systems of components with statistically dependent lifetimes. Some copulas are presented as illustrations on statistical dependence structure satisfying the sufficient condition as well.
      PubDate: 2018-05-01
      DOI: 10.1007/s00184-018-0651-6
      Issue No: Vol. 81, No. 4 (2018)
  • Stochastic comparisons of coherent systems
    • Authors: Jorge Navarro
      Pages: 465 - 482
      Abstract: The study of stochastic comparisons of coherent systems with different structures is a relevant topic in reliability theory. Several results have been obtained for specific distributions. The present paper is focused on distribution-free comparisons, that is, orderings which do not depend on the component distributions. Different assumptions for the component lifetimes are considered which lead us to different comparison techniques. Thus, if the components are independent and identically distributed (IID) or exchangeable, the orderings are obtained by using signatures. If they are just ID (homogeneous components), then ordering results for distorted distributions are used. In the general case or in the case of independent (heterogeneous) components, a similar technique based on generalized distorted distributions is applied. In these cases, the ordering results may depend on the copula used to model the dependence between the component lifetimes. Some illustrative examples are included in each case.
      PubDate: 2018-05-01
      DOI: 10.1007/s00184-018-0650-7
      Issue No: Vol. 81, No. 4 (2018)
  • Publisher Correction: Stochastic comparisons of order statistics from
           scaled and interdependent random variables
    • Authors: Chen Li; Rui Fang; Xiaohu Li
      Pages: 483 - 483
      Abstract: In the original publication of the article, the article title was incorrectly published as “Stochastic somparisons of order statistics from scaled and interdependent random variables”. However, the correct title should read “Stochastic comparisons of order statistics from scaled and interdependent random variables”.
      PubDate: 2018-05-01
      DOI: 10.1007/s00184-018-0647-2
      Issue No: Vol. 81, No. 4 (2018)
  • Nonparametric independence feature screening for ultrahigh-dimensional
           survival data
    • Authors: Jing Pan; Yuan Yu; Yong Zhou
      Abstract: With the explosion of digital information, high-dimensional data is frequently collected in prevalent domains, in which the dimension of covariates can be much larger than the sample size. Many effective methods have been developed to reduce the dimension of such data recently, however, few methods might perform well for survival data with censoring. In this article, we develop a novel nonparametric feature screening procedure based on ultrahigh-dimensional survival data by incorporating the inverse probability weighting scheme to tackle the issue of censoring. The proposed method is model-free and hence can be implemented for extensive survival models. Moreover, it is robust to heterogeneity and invariant to monotone increasing transformations of the response. The sure screening property and ranking consistency property are also established under mild conditions. The competence and robustness of our method is further confirmed through comprehensive simulation studies and an analysis of a real data example.
      PubDate: 2018-04-25
      DOI: 10.1007/s00184-018-0660-5
  • On consistency of the weighted least squares estimators in a
           semiparametric regression model
    • Authors: Xuejun Wang; Xin Deng; Shuhe Hu
      Abstract: This paper is concerned with the semiparametric regression model \(y_i=x_i\beta +g(t_i)+\sigma _ie_i,~~i=1,2,\ldots ,n,\) where \(\sigma _i^2=f(u_i)\) , \((x_i,t_i,u_i)\) are known fixed design points, \(\beta \) is an unknown parameter to be estimated, \(g(\cdot )\) and \(f(\cdot )\) are unknown functions, random errors \(e_i\) are widely orthant dependent random variables. The p-th ( \(p>0\) ) mean consistency and strong consistency for least squares estimators and weighted least squares estimators of \(\beta \) and g under some more mild conditions are investigated. A simulation study is also undertaken to assess the finite sample performance of the results that we established. The results obtained in the paper generalize and improve some corresponding ones of negatively associated random variables.
      PubDate: 2018-04-21
      DOI: 10.1007/s00184-018-0659-y
  • Hybrid estimators for small diffusion processes based on reduced data
    • Authors: Yusuke Kaino; Masayuki Uchida
      Abstract: We deal with the Bayes type estimators and the maximum likelihood type estimators of both drift and volatility parameters for small diffusion processes defined by stochastic differential equations with small perturbations from high frequency data. From the viewpoint of numerical analysis, initial Bayes type estimators for both drift and volatility parameters based on reduced data are required, and adaptive maximum likelihood type estimators with the initial Bayes type estimators, which are called hybrid estimators, are proposed. The asymptotic properties of the initial Bayes type estimators based on reduced data are derived and it is shown that the hybrid estimators have asymptotic normality and convergence of moments. Furthermore, a concrete example and simulation results are given.
      PubDate: 2018-04-19
      DOI: 10.1007/s00184-018-0657-0
  • Highest posterior mass prediction intervals for binomial and poisson
    • Authors: K. Krishnamoorthy; Shanshan Lv
      Abstract: The problems of constructing prediction intervals (PIs) for the binomial and Poisson distributions are considered. New highest posterior mass (HPM) PIs based on fiducial approach are proposed. Other fiducial PIs, an exact PI and approximate PIs are reviewed and compared with the HPM-PIs. Exact coverage studies and expected widths of prediction intervals show that the new prediction intervals are less conservative than other fiducial PIs and comparable with the approximate one based on the joint sampling approach for the binomial case. For the Poisson case, the HPM-PIs are better than the other PIs in terms of coverage probabilities and precision. The methods are illustrated using some practical examples.
      PubDate: 2018-04-11
      DOI: 10.1007/s00184-018-0658-z
  • Robust Wald-type tests for non-homogeneous observations based on the
           minimum density power divergence estimator
    • Authors: Ayanendranath Basu; Abhik Ghosh; Nirian Martin; Leandro Pardo
      Abstract: This paper considers the problem of robust hypothesis testing under non-identically distributed data. We propose Wald-type tests for both simple and composite hypothesis for independent but non-homogeneous observations based on the robust minimum density power divergence estimator of the common underlying parameter. Asymptotic and theoretical robustness properties of the proposed tests are discussed. Application to the problem of testing for the general linear hypothesis in a generalized linear model with a fixed-design has been considered in detail with specific illustrations for its special cases under the normal and Poisson distributions.
      PubDate: 2018-04-06
      DOI: 10.1007/s00184-018-0653-4
  • Shrinkage estimation in linear mixed models for longitudinal data
    • Authors: Shakhawat Hossain; Trevor Thomson; Ejaz Ahmed
      Abstract: This paper is concerned with the selection and estimation of fixed effects in linear mixed models while the random effects are treated as nuisance parameters. We propose the non-penalty James–Stein shrinkage and pretest estimation methods based on linear mixed models for longitudinal data when some of the fixed effect parameters are under a linear restriction. We establish the asymptotic distributional biases and risks of the proposed estimators, and investigate their relative performance with respect to the unrestricted maximum likelihood estimator (UE). Furthermore, we investigate the penalty (LASSO and adaptive LASSO) estimation methods and compare their relative performance with the non-penalty pretest and shrinkage estimators. A simulation study for various combinations of the inactive covariates shows that the shrinkage estimators perform better than the penalty estimators in certain parts of the parameter space. This particularly happens when there are many inactive covariates in the model. It also shows that the pretest, shrinkage, and penalty estimators all outperform the UE. We further illustrate the proposed procedures via a real data example.
      PubDate: 2018-03-30
      DOI: 10.1007/s00184-018-0656-1
  • Likelihood ratio confidence interval for the abundance under binomial
           detectability models
    • Authors: Yang Liu; Yukun Liu; Yan Fan; Han Geng
      Abstract: Binomial detectability models are often used to estimate the size or abundance of a finite population in biology, epidemiology, demography and reliability. Special cases include incompletely observed multinomial models, capture–recapture models, and distance sampling models. The most commonly-used confidence interval for the abundance is the Wald-type confidence interval, which is based on the asymptotic normality of a reasonable point estimator of the abundance. However, the Wald-type confidence interval may have poor coverage accuracy and its lower limit may be less than the number of observations. In this paper, we rigorously establish that the likelihood ratio test statistic for the abundance under the binomial detectability models follows the chisquare limiting distribution with one degree of freedom. This provides a solid theoretical justification for the use of the proposed likelihood ratio confidence interval. Our simulations indicate that in comparison to the Wald-type confidence interval, the likelihood ratio confidence interval not only has more accurate coverage rate, but also exhibits more stable performance in a variety of binomial detectability models. The proposed interval is further illustrated through analyzing three real data-sets.
      PubDate: 2018-03-30
      DOI: 10.1007/s00184-018-0655-2
  • Joint analysis of recurrent event data with additive–multiplicative
           hazards model for the terminal event time
    • Authors: Miao Han; Liuquan Sun; Yutao Liu; Jun Zhu
      Abstract: Recurrent event data are often collected in longitudinal follow-up studies. In this article, we propose a semiparametric method to model the recurrent and terminal events jointly. We present an additive–multiplicative hazards model for the terminal event and a proportional intensity model for the recurrent events, and a shared frailty is used to model the dependence between the recurrent and terminal events. We adopt estimating equation approaches for inference, and the asymptotic properties of the resulting estimators are established. The finite sample behavior of the proposed estimators is evaluated through simulation studies. An application to a medical cost study of chronic heart failure patients from the University of Virginia Health System is illustrated.
      PubDate: 2018-03-28
      DOI: 10.1007/s00184-018-0654-3
  • A complete characterization of bivariate densities using the conditional
           percentile function
    • Authors: Indranil Ghosh
      Abstract: It is well known that joint bivariate densities cannot always be characterized by the corresponding two conditional densities. Hence, additional requirements have to be imposed. In the form of a conjecture, Arnold et al. (J Multivar Anal 99:1383–1392, 2008) suggested using any one of the two conditional densities and replacing the other one by the corresponding conditional percentile function. In this article we establish, in affirmative, this conjecture and provide several illustrative examples.
      PubDate: 2018-03-21
      DOI: 10.1007/s00184-018-0652-5
  • Conditional feature screening for mean and variance functions in models
           with multiple-index structure
    • Authors: Qinqin Hu; Lu Lin
      Abstract: The existing methods for feature screening focus mainly on the mean function of regression models. The variance function, however, plays an important role in statistical theory and application. We thus investigate feature screening for mean and variance functions with multiple-index framework in high dimensional regression models. Notice that some information about predictors can be known in advance from previous investigations and experience, for example, a certain set of predictors is related to the response. Based on the conditional information, together with empirical likelihood, we propose conditional feature screening procedures. Our methods can consistently estimate the sets of active predictors in the mean and variance functions. It is interesting that the proposed screening procedures can avoid estimating the unknown link functions in the mean and variance functions, and moreover, can work well in the case of high correlation among the predictors without iterative algorithm. Therefore, our proposal is of computational simplicity. Furthermore, as a conditional method, our method is robust to the choice of the conditional set. The theoretical results reveal that the proposed procedures have sure screening properties. The attractive finite sample performance of our method is illustrated in simulations and a real data application.
      PubDate: 2018-02-16
      DOI: 10.1007/s00184-018-0646-3
  • Multi-level and mixed-level k -circulant supersaturated designs
    • Authors: K. Chatterjee; K. Drosou; S. D. Georgiou; C. Koukouvinos
      Abstract: Supersaturated designs (SSDs) constitute an important class of fractional factorial designs that could be extremely useful in factor screening experiments. Most of the existing studies have focused on balanced designs. This paper provides a new lower bound for the \(E(f_{NOD})\) -optimality measure of SSDs with general run sizes. This bound is a generalization of existing bounds since it is applicable to both balanced and unbalanced designs. Optimal multi and mixed-level, balanced and nearly balanced SSDs are constructed by applying a k-circulant type methodology. Necessary and sufficient conditions are introduced for the generator vectors, in order to pre-ensure the optimality of the constructed k-circulant SSDs. The provided lower bounds were used to measure the efficiency of the generated designs. The presented methodology leads to a number of new families of improved SSDs, providing tools for directly constructing optimal or nearly-optimal k-circulant designs by just checking the corresponding generator vector.
      PubDate: 2018-02-06
      DOI: 10.1007/s00184-018-0645-4
  • New results on quaternary codes and their Gray map images for constructing
           uniform designs
    • Authors: A. M. Elsawah; Kai-Tai Fang
      Abstract: The research of developing efficient methodologies for constructing optimal experimental designs has been very active in the last decade. Uniform design is one of the most popular approaches, carried out by filling up experimental points in a determinately uniform fashion. Applications of coding theory in experimental design are interesting and promising. Quaternary codes and their binary Gray map images attracted much attention from those researching design of experiments in recent years. The present paper aims at exploring new results for constructing uniform designs based on quaternary codes and their binary Gray map images. This paper studies the optimality of quaternary designs and their two and three binary Gray map image designs in terms of the uniformity criteria measured by: the Lee, wrap-around, symmetric, centered and mixture discrepancies. Strong relationships between quaternary designs and their two and three binary Gray map image designs are obtained, which can be used for efficiently constructing two-level designs from four-level designs and vice versa. The significance of this work is evaluated by comparing our results to the existing literature.
      PubDate: 2018-02-05
      DOI: 10.1007/s00184-018-0644-5
  • Empirical likelihood for heteroscedastic partially linear single-index
           models with growing dimensional data
    • Authors: Jianglin Fang; Wanrong Liu; Xuewen Lu
      Abstract: In this paper, we propose a new approach to the empirical likelihood inference for the parameters in heteroscedastic partially linear single-index models. In the growing dimensional setting, it is proved that estimators based on semiparametric efficient score have the asymptotic consistency, and the limit distribution of the empirical log-likelihood ratio statistic for parameters \((\beta ^{\top },\theta ^{\top })^{\top }\) is a normal distribution. Furthermore, we show that the empirical log-likelihood ratio based on the subvector of \(\beta \) is an asymptotic chi-square random variable, which can be used to construct the confidence interval or region for the subvector of \(\beta \) . The proposed method can naturally be applied to deal with pure single-index models and partially linear models with high-dimensional data. The performance of the proposed method is illustrated via a real data application and numerical simulations.
      PubDate: 2018-02-02
      DOI: 10.1007/s00184-018-0642-7
  • Optimal choice of order statistics under confidence region estimation in
           case of large samples
    • Authors: Alexander Zaigraev; Magdalena Alama-Bućko
      Abstract: The problem of optimal estimation of location and scale parameters of distributions, by means of two-dimensional confidence regions based on L-statistics, is considered. The case, when the sample size tends to infinity, is analyzed.
      PubDate: 2018-02-01
      DOI: 10.1007/s00184-018-0643-6
  • Inference for the two-parameter bathtub-shaped distribution based on
           record data
    • Authors: Mohammad Z. Raqab; Omar M. Bdair; Fahad M. Al-Aboud
      Abstract: Here we consider the record data from the two-parameter of bathtub-shaped distribution. First, we develop simplified forms for the single moments, variances and covariance of records. These distributional properties are quite useful in obtaining the best linear unbiased estimators of the location and scale parameters which can be included in the model. The estimation of the unknown shape parameters and prediction of the future unobserved records based on some observed ones are discussed. Frequentist and Bayesian analyses are adopted for conducting the estimation and prediction problems. The likelihood method, moment based method, bootstrap methods as well as the Bayesian sampling techniques are applied for the inference problems. The point predictors and credible intervals of future record values based on an informative set of records can be developed. Monte Carlo simulations are performed to compare the so developed methods and one real data set is analyzed for illustrative purposes.
      PubDate: 2018-01-05
      DOI: 10.1007/s00184-017-0641-0
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