Communications in Statistics - Theory and Methods

Journal Information
ISSN / EISSN : 0361-0926 / 1532-415X
Published by: Informa UK Limited (10.1080)
Total articles ≅ 12,975
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Communications in Statistics - Theory and Methods pp 1-28;

We consider partial linear regression models when all the variables are measured with additive distortion measurement errors. To eliminate the effect caused by the distortion, we propose the conditional mean calibration to obtain calibrated variables. A profile least squares estimator for the parameter is obtained, associated with its normal approximation based and empirical likelihood based confidence intervals. For the hypothesis testing on parameters, a restricted estimator under the null hypothesis and a test statistic are proposed. A smoothly clipped absolute deviation penalty is employed to select the relevant variables. The resulting penalized estimators are shown to be asymptotically normal and have the oracle property. Lastly, a score-type test statistic is then proposed for checking the validity of partial linear models. Simulation studies demonstrate the performance of our proposed procedure and a real example is analyzed as illustrate its practical usage.
, Gautam Choudhury
Communications in Statistics - Theory and Methods pp 1-33;

This research article investigates the stationary N-policy with a set-up time of a single server bulk arrival queueing model rendering two-heterogeneous optional repeated service (THORS) with the factor of unreliability. The server studied here is allowed to take a single vacation after each busy period following Bernoulli Schedule (BS). An extensive analysis of the proposed model is carried out using the Supplementary Variable Technique (SVT) under some suitable transformations. The joint distribution of the server’s state and queue length are obtained under both elapsed and remaining times along with their double transforms. Probability generating function (PGF) of the queue size distribution together with the mean system size of the model are determined for any arbitrary time point and service completion epoch, besides the busy period distribution and various pivotal system characteristics. A suitable linear cost structure of the underlying model is developed, and with the help of a difference operator, a locally optimal N-policy at a lower cost is obtained. Finally, some numerical experiments are carried out in support of the theory.
Peng Liu,
Communications in Statistics - Theory and Methods pp 1-20;

In this paper, the optimal maintenance strategy for the warranty product subject to multiple failure modes and repair time limit is studied from the customer’s perspective. When the product fails, a minimal repair based on the failure type is conducted. If the product can not be repaired within a given time limit, it will be replaced with a new one by the manufacturer during the warranty period. Different from the traditional renewing warranty policy, a geometric warranty policy is adopted in this work, under which once the warranty product is replaced; the length of warranty period is geometrically renewed. After the warranty expires, the product undergoes preventive maintenance (PM) periodically and the PM effect is modeled by reducing the virtual age of different failure modes by different degree. The objective is to determine the optimal interval time for PM and the optimal number of PMs by minimizing the expected life cycle cost rate of product. The existence and uniqueness of the optimal PM policy are proved theoretically, and the optimal bivariate policy can be obtained by using a recursive seeking algorithm. Numerical examples illustrate the effectiveness of geometric warranty policy and the proposed PM model.
Monika Doll,
Communications in Statistics - Theory and Methods pp 1-19;

Sample size analysis is a key part of the planning phase of any research. So far, however, hardly any literature focuses on sample size analysis methods for two-sample linear rank tests, although these methods have optimal properties for different distributions. This article provides a new sample size analysis method for linear rank tests for location shift alternatives based on score-generating functions. Results show a slightly anti-conservative behavior, no severe risk of an occurring circular argument at small to moderate variances of the population’s distribution, and good performance compared to alternate sample size analysis methods for the most well-known linear rank test, the Wilcoxon-Mann-Whitney test.
Li Wang,
Communications in Statistics - Theory and Methods pp 1-22;

In this article, we establish some results on the complete convergence and complete integral convergence for weighted sums of widely negative dependent random variables under the sub-linear expectations, which extend some complete moment convergence theorems from the classical probability space to the situation of sub-linear expectation space.
Communications in Statistics - Theory and Methods pp 1-15;

Longitudinal count models are usually constructed based on Poisson and negative binomial distributions. Recently, a single-parameter discrete Bell distribution has been presented as an alternative to well-known count distributions. In this study, a new marginal model is proposed for longitudinal count responses based on Bell distribution to handle overdispersion and dependency structure. Bell distribution is more practical in that it has fewer parameters than the negative binomial distribution and still handle overdispersion with a single parameter. Focusing on demonstrating that regression diagnostics supplement the Bell marginal model based on GEE to serve as sensitivity analysis. The Bell marginal model is used to analyze the number of accidents caused injuries in Greece during the 5-year time period. The half-normality plots indicate that the Bell marginal model provides better fit than other marginal models for the accident dataset. The common working covariance selection criterias and properties of parameter estimations are investigated for the Bell marginal model in the simulation study. Parameter estimations of the new model based on GEEs are obtained by geeM R package with the user-defined function. Diagnostic measures and simulated envelope algorithm are also provided for the proposed model.
, Lijun Wu
Communications in Statistics - Theory and Methods pp 1-32;

In this article, we consider a robust optimal proportional reinsurance and investment problem in a model with delay and dependent risks, in which the insurer’s surplus process is assumed to follow a risk model with two dependent classes of insurance business. The insurer is allowed to purchase proportional reinsurance and invest his surplus in a financial market, which contains one risk-free asset and one risky asset whose price process satisfies a jump-diffusion model. Under the consideration of the performance-related capital inflow or outflow, the insurer’s wealth process is modeled by a stochastic differential delay equation. The insurer’s aim is to develop the robust optimal reinsurance and investment strategy for the insurer by maximizing the expected exponential utility of the combination of the average historical performance and terminal wealth under the worst-case scenario of the alternative measures. By adopting the stochastic dynamic programming technique, the expressions of the robust optimal strategy and value function are explicitly obtained. Finally, we present some numerical examples to illustrate the effects of some model parameters on the optimal strategy.
Sara-Imane Zemoul,
Communications in Statistics - Theory and Methods pp 1-8;

This article is devoted to the asymptotic properties of the ordinary least squares estimator (LSE) of the coefficient ρ in a stationary autoregressive process of order one with negatively associated innovations. Under appropriate conditions, consistency and asymptotic normality are derived.
Yiwei Zong, Ffion Loring,
Communications in Statistics - Theory and Methods pp 1-9;

Gini’s rank association index is a non parametric measure of association, and is fully described by Genest, Nešlehová and Ben Ghorbal ( 2010 ). In this article, we compute the null distribution of this index up to n = 28 where n is the sample size. Our methods are based on permanents and extend the results of Betro ( 1993 ). We also discuss approximations to the null distribution for large n. We believe that Gini’s rank association index should be more widely used; in particular, it may be preferable to Spearman’s rank correlation coefficient if the bivariate distribution is such that outliers are quite likely to occur.
, Maryam Kelkinnama, Narayanaswamy Balakrishnan
Communications in Statistics - Theory and Methods pp 1-11;

In this paper, sufficient conditions are presented for comparing the residual lifetimes and inactivity times of dependent random variables at different fixed times, with respect to hazard rate, mean residual life and likelihood ratio orders. The stochastic comparisons of residual lifetimes at different random times are discussed next. Several examples are presented to illustrate the established results.
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