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 [2351 journals] |
- Spline-based quasi-likelihood estimation of mixed Poisson regression with
single-index models- Authors: Minggen Lu
Pages: 1 - 17
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: 2018-01-01
DOI: 10.1007/s00184-017-0631-2
Issue No: Vol. 81, No. 1 (2018)
- Authors: Minggen Lu
- Ordering properties of the smallest order statistics from generalized
Birnbaum–Saunders models with associated random shocks- Authors: Longxiang Fang; N. Balakrishnan
Pages: 19 - 35
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: 2018-01-01
DOI: 10.1007/s00184-017-0632-1
Issue No: Vol. 81, No. 1 (2018)
- Authors: Longxiang Fang; N. Balakrishnan
- 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
- Authors: Qinqin Hu; Lu Lin
- 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
- Authors: K. Chatterjee; K. Drosou; S. D. Georgiou; C. Koukouvinos
- 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
- Authors: A. M. Elsawah; Kai-Tai Fang
- 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
- Authors: Jianglin Fang; Wanrong Liu; Xuewen Lu
- 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
- Authors: Alexander Zaigraev; Magdalena Alama-Bućko
- 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
- Authors: Mohammad Z. Raqab; Omar M. Bdair; Fahad M. Al-Aboud
- Exact inference for Laplace distribution under progressive Type-II
censoring based on BLUEs- Authors: Kai Liu; Xiaojun Zhu; N. Balakrishnan
Abstract: In this paper, upon using the known expressions for the Best Linear Unbiased Estimators (BLUEs) of the location and scale parameters of the Laplace distribution based on a progressively Type-II right censored sample, we derive the exact moment generating function (MGF) of the linear combination of standard Laplace order statistics. By using this MGF, we obtain the exact density function of the linear combination. This density function is then utilized to develop exact marginal confidence intervals (CIs) for the location and scale parameters through some pivotal quantities. Next, we derive the exact density of the BLUEs-based quantile estimator and use it to develop exact CIs for the population quantile. A brief mention is made about the reliability and cumulative hazard functions and as to how exact CIs can be constructed for these functions based on BLUEs. A Monte Carlo simulation study is then carried out to evaluate the performance of the developed inferential results. Finally, an example is presented to illustrate the point and interval estimation methods developed here.
PubDate: 2018-01-03
DOI: 10.1007/s00184-017-0640-1
- Authors: Kai Liu; Xiaojun Zhu; N. Balakrishnan
- Modularization of hybrid censoring schemes and its application to unified
progressive hybrid censoring- Authors: Julian Górny; Erhard Cramer
Abstract: In this paper, a structural analysis of hybrid censoring models is presented. This new modularization approach to hybrid censoring models enables a convenient derivation of distributional results. For instance, it allows to derive the exact distribution of the MLEs under an exponential assumption for very complex hybrid scenarios. In order to illustrate the benefit of this idea, we apply it to four new unified progressive hybrid censoring schemes. They are extensions of already proposed unified Type-I/II/III/IV hybrid censoring schemes to progressively Type-II censored data. The resulting analysis shows that the modularization approach provides a powerful, efficient, and elegant tool to study even more complex hybrid censoring models.
PubDate: 2017-12-06
DOI: 10.1007/s00184-017-0639-7
- Authors: Julian Górny; Erhard Cramer
- An EM algorithm for the destructive COM-Poisson regression cure rate model
- Authors: Suvra Pal; Jacob Majakwara; N. Balakrishnan
Abstract: In this paper, we consider a competitive scenario and assume the initial number of competing causes to undergo a destruction after an initial treatment. This brings in a more realistic and practical interpretation of the biological mechanism of the occurrence of tumor since what is recorded is only from the undamaged portion of the original number of competing causes. Instead of assuming any particular distribution for the competing cause, we assume the competing cause to follow a Conway–Maxwell Poisson distribution which brings in flexibility as it can handle both over-dispersion and under-dispersion that we usually encounter in count data. Under this setup and assuming a Weibull distribution to model the time-to-event, we develop the expectation maximization algorithm for such a flexible destructive cure rate model. An extensive simulation study is carried out to demonstrate the performance of the proposed estimation method. Finally, a melanoma data is analyzed for illustrative purpose.
PubDate: 2017-12-06
DOI: 10.1007/s00184-017-0638-8
- Authors: Suvra Pal; Jacob Majakwara; N. Balakrishnan
- Relations for product moments and covariances of k th records from
discrete distributions- Authors: Krzysztof Jasiński
Abstract: The aim of this paper is to establish recurrence relations satisfied by product moments and covariances of kth records arising from discrete distributions. They will be evaluated for geometric underlying distribution. Then we use these results to obtain formulas for correlation coefficients of geometric kth records. We consider all three known types of kth records: strong, ordinary, and weak.
PubDate: 2017-11-30
DOI: 10.1007/s00184-017-0637-9
- Authors: Krzysztof Jasiński
- 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
- 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
- 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
- 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