Metrika [SJR: 0.605] [H-I: 30] [4 followers] Follow Hybrid journal (It can contain Open Access articles) ISSN (Print) 1435-926X - ISSN (Online) 0026-1335 Published by Springer-Verlag [2354 journals] |
- Stationary bootstrapping for common mean change detection in
cross-sectionally dependent panels- Authors: Eunju Hwang; Dong Wan Shin
Pages: 767 - 787
Abstract: Stationary bootstrapping is applied to a CUSUM test for common mean break detection in cross-sectionally correlated panel data. Asymptotic null distribution of the bootstrapped test is derived, which is the same as that of the original CUSUM test depending on cross-sectional correlation parameter. A bootstrap test using the CUSUM test with bootstrap critical values is proposed and its asymptotic validity is proved. Finite sample Monte-Carlo simulation shows that the proposed test has reasonable size while other existing tests have severe size distortion under cross-section correlation. The simulation also shows good power performance of the proposed test against non-cancelling mean changes. The simulation also shows that the theoretically justified stationary bootstrapping CUSUM test has comparable size and power relative to other, theoretically unjustified, moving block or tapered block bootstrapping CUSUM tests.
PubDate: 2017-11-01
DOI: 10.1007/s00184-017-0627-y
Issue No: Vol. 80, No. 6-8 (2017)
- Authors: Eunju Hwang; Dong Wan Shin
- Three-stage confidence intervals for a linear combination of locations of
two negative exponential distributions- Authors: Eiichi Isogai; Chikara Uno
Abstract: Mukhopadhyay and Padmanabhan (Metrika 40:121–128, 1993) considered the construction of fixed-width confidence intervals for the difference of location parameters of two negative exponential distributions via triple sampling when the scale parameters are unknown and unequal. Under the same setting, this paper deals with the problem of fixed-width confidence interval estimation for a linear combination of location parameters, using the above mentioned three-stage procedure.
PubDate: 2017-11-24
DOI: 10.1007/s00184-017-0635-y
- Authors: Eiichi Isogai; Chikara Uno
- On stochastic comparisons of minimum order statistics from the
location–scale family of distributions- Authors: Nil Kamal Hazra; Mithu Rani Kuiti; Maxim Finkelstein; Asok K. Nanda
Abstract: We consider stochastic comparisons of minimum order statistics from the location–scale family of distributions that contain most of the popular lifetime distributions. Under certain assumptions, we show that the minimum order statistic of one set of random variables dominates that of another set of random variables with respect to different stochastic orders. Furthermore, we illustrate our results using some well-known specific distributions.
PubDate: 2017-11-21
DOI: 10.1007/s00184-017-0636-x
- Authors: Nil Kamal Hazra; Mithu Rani Kuiti; Maxim Finkelstein; Asok K. Nanda
- Nonparametric estimation of conditional distribution functions with
longitudinal data and time-varying parametric models- Authors: Mohammed Chowdhury; Colin Wu; Reza Modarres
Abstract: Nonparametric estimation and inferences of conditional distribution functions with longitudinal data have important applications in biomedical studies. We propose in this paper an estimation approach based on time-varying parametric models. Our model assumes that the conditional distribution of the outcome variable at each given time point can be approximated by a parametric model, but the parameters are smooth functions of time. Our estimation is based on a two-step smoothing method, in which we first obtain the raw estimators of the conditional distribution functions at a set of disjoint time points, and then compute the final estimators at any time by smoothing the raw estimators. Asymptotic properties, including the asymptotic biases, variances and mean squared errors, are derived for the local polynomial smoothed estimators. Applicability of our two-step estimation method is demonstrated through a large epidemiological study of childhood growth and blood pressure. Finite sample properties of our procedures are investigated through simulation study.
PubDate: 2017-11-09
DOI: 10.1007/s00184-017-0634-z
- Authors: Mohammed Chowdhury; Colin Wu; Reza Modarres
- A residual inaccuracy measure based on the relevation transform
- Authors: Georgios Psarrakos; Antonio Di Crescenzo
Abstract: Inaccuracy and information measures based on the cumulative residual entropy are useful in various fields, and are attracting increasing attention in Probability Theory and Statistics. In this paper, we introduce and study an inaccuracy measure concerning the relevation transform of two nonnegative continuous random variables. We investigate various distributional properties and characterization results that are based on the mean residual lifetime and involve the generalized Pareto distribution. A connection with the proportional hazards model is also provided. We obtain comparison results involving the proposed inaccuracy measure and some existing inaccuracy measures. Some illustrative examples are finally given.
PubDate: 2017-11-05
DOI: 10.1007/s00184-017-0633-0
- Authors: Georgios Psarrakos; Antonio Di Crescenzo
- Ordering properties of the smallest order statistics from generalized
Birnbaum–Saunders models with associated random shocks- Authors: Longxiang Fang; N. Balakrishnan
Abstract: Let \(X_{1},\ldots , X_{n}\) be lifetimes of components with independent non-negative generalized Birnbaum–Saunders random variables with shape parameters \(\alpha _{i}\) and scale parameters \(\beta _{i},~ i=1,\ldots ,n\) , and \(I_{p_{1}},\ldots , I_{p_{n}}\) be independent Bernoulli random variables, independent of \(X_{i}\) ’s, with \(E(I_{p_{i}})=p_{i},~i=1,\ldots ,n\) . These are associated with random shocks on \(X_{i}\) ’s. Then, \(Y_{i}=I_{p_{i}}X_{i}, ~i=1,\ldots ,n,\) correspond to the lifetimes when the random shock does not impact the components and zero when it does. In this paper, we discuss stochastic comparisons of the smallest order statistic arising from such random variables \(Y_{i},~i=1,\ldots ,n\) . When the matrix of parameters \((h({\varvec{p}}), {\varvec{\beta }}^{\frac{1}{\nu }})\) or \((h({\varvec{p}}), {\varvec{\frac{1}{\alpha }}})\) changes to another matrix of parameters in a certain mathematical sense, we study the usual stochastic order of the smallest order statistic in such a setup. Finally, we apply the established results to two special cases: classical Birnbaum–Saunders and logistic Birnbaum–Saunders distributions.
PubDate: 2017-10-20
DOI: 10.1007/s00184-017-0632-1
- Authors: Longxiang Fang; N. Balakrishnan
- Spline-based quasi-likelihood estimation of mixed Poisson regression with
single-index models- Authors: Minggen Lu
Abstract: We consider spline-based quasi-likelihood estimation for mixed Poisson regression with single-index models. The unknown smooth function is approximated by B-splines, and a modified Fisher scoring algorithm is employed to compute the estimates. The spline estimate of the nonparametric component is shown to achieve the optimal rate of convergence, and the asymptotic normality of the regression parameter estimates is still valid even if the variance function is misspecified. The semiparametric efficiency of the model can be established if the variance function is correctly specified. The variance of the regression parameter estimates can be consistently estimated by a simple procedure based on the least-squares estimation. The proposed method is evaluated via an extensive Monte Carlo study, and the methodology is illustrated on an air pollution study.
PubDate: 2017-10-16
DOI: 10.1007/s00184-017-0631-2
- Authors: Minggen Lu
- Universally optimal designs under mixed interference models with and
without block effects- Authors: Katarzyna Filipiak; Augustyn Markiewicz
Abstract: The literature on neighbor designs as introduced by Rees (Biometrics 23:779–791, 1967) is mainly devoted to construction methods, providing few results on their statistical properties, such as efficiency and optimality. A review of the available literature, with special emphasis on the optimality of neighbor designs under various fixed effects interference models, is given in Filipiak and Markiewicz (Commun Stat Theory Methods 46:1127–1143, 2017). The aim of this paper is to verify whether the designs presented by Filipiak and Markiewicz (2017) as universally optimal under fixed interference models are still universally optimal under models with random interference effects. Moreover, it is shown that for a specified covariance matrix of random interference effects, a universally optimal design under mixed interference models with block effects is universally optimal over a wider class of designs. In this paper the method presented by Filipiak and Markiewicz (Metrika 65:369–386, 2007) is extended and then applied to mixed interference models without or with block effects.
PubDate: 2017-10-14
DOI: 10.1007/s00184-017-0628-x
- Authors: Katarzyna Filipiak; Augustyn Markiewicz
- Exact inference for the difference of Laplace location parameters
- Authors: Maria Tafiadi; George Iliopoulos
Abstract: We consider exact procedures for testing the equality of means (location parameters) of two Laplace populations with equal scale parameters based on corresponding independent random samples. The test statistics are based on either the maximum likelihood estimators or the best linear unbiased estimators of the Laplace parameters. By conditioning on certain quantities we manage to express their exact distributions as mixtures of ratios of linear combinations of standard exponential random variables. This allows us to find their exact quantiles and tabulate them for several sample sizes. The powers of the tests are compared either numerically or by simulation. Exact confidence intervals for the difference of the means corresponding to those tests are also constructed. The exact procedures are illustrated via a real data example.
PubDate: 2017-10-10
DOI: 10.1007/s00184-017-0630-3
- Authors: Maria Tafiadi; George Iliopoulos
- Adjusted Pearson Chi-Square feature screening for multi-classification
with ultrahigh dimensional data- Authors: Lyu Ni; Fang Fang; Fangjiao Wan
Abstract: Huang et al. (J Bus Econ Stat 32:237–244, 2014) first proposed a Pearson Chi-Square based feature screening procedure tailored to multi-classification problem with ultrahigh dimensional categorical covariates, which is a common problem in practice but has seldom been discussed in the literature. However, their work establishes the sure screening property only in a limited setting. Moreover, the p value based adjustments when the number of categories involved by each covariate is different do not work well in several practical situations. In this paper, we propose an adjusted Pearson Chi-Square feature screening procedure and a modified method for tuning parameter selection. Theoretically, we establish the sure screening property of the proposed method in general settings. Empirically, the proposed method is more successful than Pearson Chi-Square feature screening in handling non-equal numbers of covariate categories in finite samples. Results of three simulation studies and one real data analysis are presented. Our work together with Huang et al. (J Bus Econ Stat 32:237–244, 2014) establishes a solid theoretical foundation and empirical evidence for the family of Pearson Chi-Square based feature screening methods.
PubDate: 2017-10-07
DOI: 10.1007/s00184-017-0629-9
- Authors: Lyu Ni; Fang Fang; Fangjiao Wan
- Stochastic comparisons of order statistics from heterogeneous random
variables with Archimedean copula- Authors: M. Mesfioui; M. Kayid; S. Izadkhah
Abstract: This article is devoted to characterize several ordering properties of the maximum order statistic of heterogenous random variables with an Archimedean copula. Some examples are also included to illustrate the obtained results.
PubDate: 2017-10-03
DOI: 10.1007/s00184-017-0626-z
- Authors: M. Mesfioui; M. Kayid; S. Izadkhah
- Multivariate saddlepoint tests on the mean direction of the von
Mises–Fisher distribution- Authors: R. Gatto
Abstract: This article provides P values for two new tests on the mean direction of the von Mises–Fisher distribution. The test statistics are obtained from the exponent of the saddlepoint approximation to the density of M-estimators, as suggested by Robinson et al. (Ann Stat 31:1154–1169, 2003). These test statistics are chi-square distributed with asymptotically small relative errors. Despite the high dimensionality of the problem, the proposed P values are accurate and simple to compute. The numerical precision of the P values of the new tests is illustrated by some simulation studies.
PubDate: 2017-09-13
DOI: 10.1007/s00184-017-0625-0
- Authors: R. Gatto
- R-optimal designs for multi-factor models with heteroscedastic errors
- Authors: Lei He; Rong-Xian Yue
Abstract: In this paper, we consider the R-optimal design problem for multi-factor regression models with heteroscedastic errors. It is shown that a R-optimal design for the heteroscedastic Kronecker product model is given by the product of the R-optimal designs for the marginal one-factor models. However, R-optimal designs for the additive models can be constructed from R-optimal designs for the one-factor models only if sufficient conditions are satisfied. Several examples are presented to illustrate and check optimal designs based on R-optimality criterion.
PubDate: 2017-08-02
DOI: 10.1007/s00184-017-0624-1
- Authors: Lei He; Rong-Xian Yue
- Estimating moments in ANOVA-type mixed models
- Authors: Zaixing Li; Fei Chen; Lixing Zhu
Abstract: In the paper, a simple projection-based method is systematically developed to estimate the qth ( \(q\ge 2\) ) order moments of random effects and errors in the ANOVA type mixed model (ANOVAMM), where the response may not be divided into independent sub-vectors. All the estimates are weakly consistent and the second-order moment estimates are strongly consistent. Besides, the derived estimates are different from those in mixed models with cluster design. Simulation studies are conducted to examine the finite sample performance of the estimates and two real data examples are analyzed for illustration.
PubDate: 2017-08-02
DOI: 10.1007/s00184-017-0623-2
- Authors: Zaixing Li; Fei Chen; Lixing Zhu
- Some general points on the $$I^2$$ I 2 -measure of heterogeneity in
meta-analysis- Authors: Dankmar Böhning; Rattana Lerdsuwansri; Heinz Holling
Abstract: Meta-analysis has developed to be a most important tool in evaluation research. Heterogeneity is an issue that is present in almost any meta-analysis. However, the magnitude of heterogeneity differs across meta-analyses. In this respect, Higgins’ \(I^2\) has emerged to be one of the most used and, potentially, one of the most useful measures as it provides quantification of the amount of heterogeneity involved in a given meta-analysis. Higgins’ \(I^2\) is conventionally interpreted, in the sense of a variance component analysis, as the proportion of total variance due to heterogeneity. However, this interpretation is not entirely justified as the second part involved in defining the total variation, usually denoted as \(s^2\) , is not an average of the study-specific variances, but in fact some other function of the study-specific variances. We show that \(s^2\) is asymptotically identical to the harmonic mean of the study-specific variances and, for any number of studies, is at least as large as the harmonic mean with the inequality being sharp if all study-specific variances agree. This justifies, from our point of view, the interpretation of explained variance, at least for meta-analyses with larger number of component studies or small variation in study-specific variances. These points are illustrated by a number of empirical meta-analyses as well as simulation work.
PubDate: 2017-07-22
DOI: 10.1007/s00184-017-0622-3
- Authors: Dankmar Böhning; Rattana Lerdsuwansri; Heinz Holling
- Multidimensional strong large deviation results
- Authors: Cyrille Joutard
Abstract: We establish strong large deviation results for an arbitrary sequence of random vectors under some assumptions on the normalized cumulant generating function. In other words, we give asymptotic approximations for a multivariate tail probability of the same kind as the one obtained by Bahadur and Rao (Ann Math Stat 31:1015–1027, 1960) for the sample mean (in the one-dimensional case). The proof of our results follows the same lines as in Chaganty and Sethuraman (J Stat Plan Inference, 55:265–280, 1996). We also present three statistical applications to illustrate our results, the first one dealing with a vector of independent sample variances, the second one with a Gaussian multiple linear regression model and the third one with the multivariate Nadaraya–Watson estimator. Some numerical results are also presented for the first two applications.
PubDate: 2017-07-15
DOI: 10.1007/s00184-017-0621-4
- Authors: Cyrille Joutard
- A new measure of association between random variables
- Authors: Majid Asadi
Abstract: We propose a new measure of association between two continuous random variables X and Y based on the covariance between X and the log-odds rate associated to Y. The proposed index of correlation lies in the range [ \(-1\) , 1]. We show that the extremes of the range, i.e., \(-1\) and 1, are attainable by the Fr \(\acute{\mathrm{e}}\) chet bivariate minimal and maximal distributions, respectively. It is also shown that if X and Y have bivariate normal distribution, the resulting measure of correlation equals the Pearson correlation coefficient \(\rho \) . Some interpretations and relationships to other variability measures are presented. Among others, it is shown that for non-negative random variables the proposed association measure can be represented in terms of the mean residual and mean inactivity functions. Some illustrative examples are also provided.
PubDate: 2017-07-03
DOI: 10.1007/s00184-017-0620-5
- Authors: Majid Asadi
- Stochastic comparisons of distorted distributions, coherent systems and
mixtures with ordered components- Authors: Jorge Navarro; Yolanda del Águila
Abstract: A distribution function F is a generalized distorted distribution of the distribution functions \(F_1,\ldots ,F_n\) if \(F=Q(F_1,\ldots ,F_n)\) for an increasing continuous distortion function Q such that \(Q(0,\ldots ,0)=0\) and \(Q(1,\ldots ,1)=1\) . In this paper, necessary and sufficient conditions for the stochastic (ST) and the hazard rate (HR) orderings of generalized distorted distributions are provided when the distributions \(F_1,\ldots ,F_n\) are ordered. These results are used to obtain distribution-free ordering properties for coherent systems with heterogeneous components. In particular, we determine all the ST and HR orderings for coherent systems with 1–3 independent components. We also compare systems with dependent components. The results on distorted distributions are also used to get comparisons of finite mixtures.
PubDate: 2017-06-28
DOI: 10.1007/s00184-017-0619-y
- Authors: Jorge Navarro; Yolanda del Águila
- Weak and strong laws of large numbers for arrays of rowwise END random
variables and their applications- Authors: Aiting Shen; Andrei Volodin
Abstract: In the paper, the Marcinkiewicz–Zygmund type moment inequality for extended negatively dependent (END, in short) random variables is established. Under some suitable conditions of uniform integrability, the \(L_r\) convergence, weak law of large numbers and strong law of large numbers for usual normed sums and weighted sums of arrays of rowwise END random variables are investigated by using the Marcinkiewicz–Zygmund type moment inequality. In addition, some applications of the \(L_r\) convergence, weak and strong laws of large numbers to nonparametric regression models based on END errors are provided. The results obtained in the paper generalize or improve some corresponding ones for negatively associated random variables and negatively orthant dependent random variables.
PubDate: 2017-05-22
DOI: 10.1007/s00184-017-0618-z
- Authors: Aiting Shen; Andrei Volodin
- Minimum distance estimators for count data based on the probability
generating function with applications- Authors: M. D. Jiménez-Gamero; A. Batsidis
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